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<ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="17"/> </region> <region region-id="286" left="24" top="668.25" width="168" height="12" align-x="30" align-y="678" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> (GIVEN-MINERR) sau (GIVEN-FIND) </text> </region> <region region-id="287" left="24" top="681" width="24" height="12.75" align-x="35.25" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="288" left="72" top="681" width="25.5" height="12.75" align-x="84.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="289" left="132" top="681" width="24" height="12.75" align-x="143.25" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">c</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="290" left="24" top="699" width="24" height="12.75" align-x="35.25" align-y="708" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Given</ml:id> </math> <rendering item-idref="21"/> </region> <region region-id="291" left="12" top="727.5" width="288" height="43.5" align-x="225" align-y="750" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">a</ml:id> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> <ml:real>4</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">b</ml:id> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> <ml:real>3</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">c</ml:id> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:apply> </math> <rendering item-idref="22"/> </region> <region region-id="292" left="12" top="781.5" width="288" height="43.5" align-x="225" align-y="804" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">a</ml:id> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> <ml:real>3</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">b</ml:id> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">c</ml:id> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> <ml:real>1</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:apply> </math> <rendering item-idref="23"/> </region> <region region-id="293" left="12" top="835.5" width="264" height="43.5" align-x="225" align-y="858" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">a</ml:id> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">b</ml:id> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> <ml:real>1</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">c</ml:id> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> <ml:real>0</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:apply> </math> <rendering item-idref="24"/> </region> <region region-id="294" left="18" top="886.5" width="93" height="45.75" align-x="43.5" align-y="912" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:matrix> <ml:apply> <ml:Minerr auto-method="true" method="linear" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:sequence> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="295" left="18" top="945" width="44.25" height="12.75" align-x="27.75" align-y="954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-6.7800000000000029</ml:real> </result> </ml:eval> </math> <rendering item-idref="26"/> </region> <region region-id="296" left="114" top="945" width="33.75" height="12.75" align-x="125.25" align-y="954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>69</ml:real> </result> </ml:eval> </math> <rendering item-idref="27"/> </region> <region region-id="297" left="192" top="945" width="27.75" height="12.75" align-x="201.75" align-y="954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">c</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.0000000000000568</ml:real> </result> </ml:eval> </math> <rendering item-idref="28"/> </region> <region region-id="298" left="18" top="962.25" width="144" height="12" align-x="36.75" align-y="972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> construim functia de aproximare: </text> </region> <region region-id="299" left="186" top="963" width="105" height="18.75" align-x="225.75" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">aprox</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">z</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">c</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="300" left="24" top="1002" width="378" height="258.75" align-x="24" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="30"/> <rendering item-idref="31"/> </region> <region region-id="301" left="12" top="1280.25" width="221.25" height="12" align-x="37.5" align-y="1290" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Aproximarea folosind functii predefinite in Mathcad </text> </region> <region region-id="302" left="180" top="1352.25" width="237" height="24" align-x="183.75" align-y="1362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Sa se aproximeze functia exponentiala de legatura dintre marimile de intrare (X) si rezultatele obtinute (Y) </text> </region> <region region-id="303" left="24" top="1301.25" width="39" height="128.25" align-x="37.5" align-y="1368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">X</ml:id> <ml:matrix rows="8" cols="1"> <ml:real>1</ml:real> <ml:real>2</ml:real> <ml:real>3</ml:real> <ml:real>4</ml:real> <ml:real>5</ml:real> <ml:real>6</ml:real> <ml:real>7</ml:real> <ml:real>8</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="304" left="114" top="1301.25" width="42.75" height="128.25" align-x="126.75" align-y="1368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Y</ml:id> <ml:matrix rows="8" cols="1"> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>4</ml:real> <ml:real>9</ml:real> <ml:real>24</ml:real> <ml:real>45</ml:real> <ml:real>50</ml:real> <ml:real>80</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="305" left="18" top="1442.25" width="221.25" height="12" align-x="30" align-y="1452" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> =pentru aproximare, folosim o functie exponentiala: </text> </region> <region region-id="306" left="24" top="1459.5" width="122.25" height="25.5" align-x="45.75" align-y="1476" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="34"/> </region> <region region-id="307" left="186" top="1466.25" width="224.25" height="12" align-x="207.75" align-y="1476" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> coeficientii se exprima cu functia predefinita EXPFIT </text> </region> <region region-id="308" left="24" top="1490.25" width="216.75" height="12" align-x="39" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> definim coeficientii, dandu-le o valoare (de evitat 0) </text> </region> <region region-id="309" left="30" top="1510.5" width="51" height="45.75" align-x="55.5" align-y="1536" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <ml:matrix rows="3" cols="1"> <ml:real>1</ml:real> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="310" left="24" top="1562.25" width="69" height="12" align-x="38.25" align-y="1572" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> =apelam functia </text> </region> <region region-id="311" left="24" top="1575" width="103.5" height="12.75" align-x="49.5" align-y="1584" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <ml:apply> <ml:id xml:space="preserve">expfit</ml:id> <ml:sequence> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">coef</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="36"/> </region> <region region-id="312" left="24" top="1594.5" width="80.25" height="45.75" align-x="48" align-y="1620" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>7.0596483729587511</ml:real> <ml:real>0.31939073792635175</ml:real> <ml:real>-11.321170122990633</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="37"/> </region> <region region-id="313" left="24" top="1640.25" width="171" height="12" align-x="36" align-y="1650" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> reprez grafic functia, dupa ce o definim </text> </region> <region region-id="314" left="30" top="1657.5" width="135.75" height="25.5" align-x="53.25" align-y="1674" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">z</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:define> </math> <rendering item-idref="38"/> </region> <region region-id="315" left="36" top="1692" width="242.25" height="189.75" align-x="36" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="39"/> <rendering item-idref="40"/> </region> <region region-id="316" left="186" top="1952.25" width="237" height="24" align-x="189.75" align-y="1962" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Sa se aproximeze functia logaritmica de legatura dintre marimile de intrare (X) si rezultatele obtinute (Y) </text> </region> <region region-id="317" left="30" top="1901.25" width="39" height="128.25" align-x="43.5" align-y="1968" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">X</ml:id> <ml:matrix rows="8" cols="1"> <ml:real>1</ml:real> <ml:real>2</ml:real> <ml:real>3</ml:real> <ml:real>4</ml:real> <ml:real>5</ml:real> <ml:real>6</ml:real> <ml:real>7</ml:real> <ml:real>8</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="318" left="120" top="1901.25" width="42.75" height="128.25" align-x="132.75" align-y="1968" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Y</ml:id> <ml:matrix rows="8" cols="1"> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>4</ml:real> <ml:real>9</ml:real> <ml:real>24</ml:real> <ml:real>45</ml:real> <ml:real>50</ml:real> <ml:real>80</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="42"/> </region> <region region-id="319" left="18" top="2048.25" width="217.5" height="12" align-x="30" align-y="2058" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> =pentru aproximare, folosim o functie logaritmica: </text> </region> <region region-id="320" left="12" top="2073" width="164.25" height="18" align-x="53.25" align-y="2082" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="logfit">f</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ln</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">z</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="43"/> </region> <region region-id="321" left="186" top="2072.25" width="231.75" height="12" align-x="207.75" align-y="2082" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> coeficientii se exprima cu functia predefinita LOGFIT </text> </region> <region region-id="322" left="24" top="2096.25" width="222.75" height="12" align-x="39" align-y="2106" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> definim coeficientii, dandu-le o valoare (de evitat 0) </text> </region> <region region-id="323" left="30" top="2116.5" width="51" height="45.75" align-x="55.5" align-y="2142" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <ml:matrix rows="3" cols="1"> <ml:real>1</ml:real> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="44"/> </region> <region region-id="324" left="24" top="2168.25" width="69.75" height="12" align-x="38.25" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> =apelam functia </text> </region> <region region-id="325" left="24" top="2181" width="102.75" height="12.75" align-x="49.5" align-y="2190" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <ml:apply> <ml:id xml:space="preserve">logfit</ml:id> <ml:sequence> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">coef</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="326" left="24" top="2197.5" width="100.5" height="63.75" align-x="48" align-y="2232" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>29774.768526458975</ml:real> <ml:real>2697.095358179708</ml:real> <ml:real>-235241.22697158987</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="46"/> </region> <region region-id="327" left="18" top="2264.25" width="171" height="12" align-x="30" align-y="2274" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> reprez grafic functia, dupa ce o definim </text> </region> <region region-id="328" left="24" top="2283" width="174" height="18" align-x="66.75" align-y="2292" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="logfit">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ln</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">z</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="329" left="30" top="2316" width="261" height="189.75" align-x="30" align-y="2316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="48"/> <rendering item-idref="49"/> </region> <region region-id="330" left="18" top="2529" width="72.75" height="12.75" align-x="43.5" align-y="2538" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <ml:apply> <ml:id xml:space="preserve">line</ml:id> <ml:sequence> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">Y</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="331" left="162" top="2540.25" width="242.25" height="12" align-x="183.75" align-y="2550" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> aproximare liniara - bazata pe eroarea minima patratica </text> </region> <region region-id="332" left="18" top="2553" width="109.5" height="18" align-x="54" align-y="2562" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="line">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="333" left="18" top="2577" width="83.25" height="12.75" align-x="43.5" align-y="2586" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <ml:apply> <ml:id xml:space="preserve">medfit</ml:id> <ml:sequence> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">Y</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="52"/> </region> <region region-id="334" left="162" top="2582.25" width="259.5" height="12" align-x="162" align-y="2592" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> aproximare liniara - bazata pe regresiune mediana-mediana </text> </region> <region region-id="335" left="18" top="2595" width="120" height="18" align-x="64.5" align-y="2604" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="medfit">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="53"/> </region> <region region-id="336" left="18" top="2628" width="333" height="249.75" align-x="18" align-y="2628" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="54"/> <rendering item-idref="55"/> </region> <region region-id="337" left="12" top="2912.25" width="130.5" height="12" align-x="27" align-y="2922" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> =definim o functie ajutatoare: </text> </region> <region region-id="338" left="150" top="2899.5" width="52.5" height="51.75" align-x="173.25" align-y="2928" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">F</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">x</ml:id> <ml:real>1</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="56"/> </region> <region region-id="339" left="12" top="2954.25" width="158.25" height="12" align-x="21" align-y="2964" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> coef se obtin apeland functia LINFIT </text> </region> <region region-id="340" left="18" top="2973" width="86.25" height="12.75" align-x="43.5" align-y="2982" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <ml:apply> <ml:id xml:space="preserve">linfit</ml:id> <ml:sequence> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">F</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="57"/> </region> <region region-id="341" left="24" top="2998.5" width="75.75" height="45.75" align-x="48" align-y="3024" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> 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xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">b</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ErrMedPat</ml:id> <ml:sequence> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="16"/> </region> <region region-id="285" left="276" top="517.5" width="103.5" height="29.25" align-x="367.5" align-y="534" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">c</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">ErrMedPat</ml:id> <ml:sequence> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:sequence> </ml:apply> </ml:lambda> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="17"/> </region> <region region-id="286" left="24" top="668.25" width="168" height="12" align-x="30" align-y="678" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> (GIVEN-MINERR) sau (GIVEN-FIND) </text> </region> <region region-id="287" left="24" top="681" width="24" height="12.75" align-x="35.25" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="18"/> 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<ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">b</ml:id> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> <ml:real>1</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">c</ml:id> <ml:parens> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> <ml:real>0</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:apply> </math> <rendering item-idref="24"/> </region> <region region-id="294" left="18" top="886.5" width="93" height="45.75" align-x="43.5" align-y="912" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:matrix> <ml:apply> <ml:Minerr auto-method="true" method="linear" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:sequence> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="295" left="18" top="945" width="44.25" height="12.75" align-x="27.75" align-y="954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-6.7800000000000029</ml:real> </result> </ml:eval> </math> <rendering item-idref="26"/> </region> <region region-id="296" left="114" top="945" width="33.75" height="12.75" align-x="125.25" align-y="954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>69</ml:real> </result> </ml:eval> </math> <rendering item-idref="27"/> </region> <region region-id="297" left="192" top="945" width="27.75" height="12.75" align-x="201.75" align-y="954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">c</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.0000000000000568</ml:real> </result> </ml:eval> </math> <rendering item-idref="28"/> </region> <region region-id="298" left="18" top="962.25" width="144" height="12" align-x="36.75" align-y="972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> construim functia de aproximare: </text> </region> <region region-id="299" left="186" top="963" width="105" height="18.75" align-x="225.75" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">aprox</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">z</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">c</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="300" left="24" top="1002" width="378" height="258.75" align-x="24" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="30"/> <rendering item-idref="31"/> </region> <region region-id="301" left="12" top="1280.25" width="221.25" height="12" align-x="37.5" align-y="1290" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Aproximarea folosind functii predefinite in Mathcad </text> </region> <region region-id="302" left="180" top="1352.25" width="237" height="24" align-x="183.75" align-y="1362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Sa se aproximeze functia exponentiala de legatura dintre marimile de intrare (X) si rezultatele obtinute (Y) </text> </region> <region region-id="303" left="24" top="1301.25" width="39" height="128.25" align-x="37.5" align-y="1368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">X</ml:id> <ml:matrix rows="8" cols="1"> <ml:real>1</ml:real> <ml:real>2</ml:real> <ml:real>3</ml:real> <ml:real>4</ml:real> <ml:real>5</ml:real> <ml:real>6</ml:real> <ml:real>7</ml:real> <ml:real>8</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="304" left="114" top="1301.25" width="42.75" height="128.25" align-x="126.75" align-y="1368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Y</ml:id> <ml:matrix rows="8" cols="1"> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>4</ml:real> <ml:real>9</ml:real> <ml:real>24</ml:real> <ml:real>45</ml:real> <ml:real>50</ml:real> <ml:real>80</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="305" left="18" top="1442.25" width="221.25" height="12" align-x="30" align-y="1452" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> =pentru aproximare, folosim o functie exponentiala: </text> </region> <region region-id="306" left="24" top="1459.5" width="122.25" height="25.5" align-x="45.75" align-y="1476" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="34"/> </region> <region region-id="307" left="186" top="1466.25" width="224.25" height="12" align-x="207.75" align-y="1476" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> coeficientii se exprima cu functia predefinita EXPFIT </text> </region> <region region-id="308" left="24" top="1490.25" width="216.75" height="12" align-x="39" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> definim coeficientii, dandu-le o valoare (de evitat 0) </text> </region> <region region-id="309" left="30" top="1510.5" width="51" height="45.75" align-x="55.5" align-y="1536" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <ml:matrix rows="3" cols="1"> <ml:real>1</ml:real> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="310" left="24" top="1562.25" width="69" height="12" align-x="38.25" align-y="1572" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> =apelam functia </text> </region> <region region-id="311" left="24" top="1575" width="103.5" height="12.75" align-x="49.5" align-y="1584" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <ml:apply> <ml:id xml:space="preserve">expfit</ml:id> <ml:sequence> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">coef</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="36"/> </region> <region region-id="312" left="24" top="1594.5" width="80.25" height="45.75" align-x="48" align-y="1620" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>7.0596483729587511</ml:real> <ml:real>0.31939073792635175</ml:real> <ml:real>-11.321170122990633</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="37"/> </region> <region region-id="313" left="24" top="1640.25" width="171" height="12" align-x="36" align-y="1650" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> reprez grafic functia, dupa ce o definim </text> </region> <region region-id="314" left="30" top="1657.5" width="135.75" height="25.5" align-x="53.25" align-y="1674" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">z</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:define> </math> <rendering item-idref="38"/> </region> <region region-id="315" left="36" top="1692" width="242.25" height="189.75" align-x="36" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="39"/> <rendering item-idref="40"/> </region> <region region-id="316" left="186" top="1952.25" width="237" height="24" align-x="189.75" align-y="1962" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Sa se aproximeze functia logaritmica de legatura dintre marimile de intrare (X) si rezultatele obtinute (Y) </text> </region> <region region-id="317" left="30" top="1901.25" width="39" height="128.25" align-x="43.5" align-y="1968" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">X</ml:id> <ml:matrix rows="8" cols="1"> <ml:real>1</ml:real> <ml:real>2</ml:real> <ml:real>3</ml:real> <ml:real>4</ml:real> <ml:real>5</ml:real> <ml:real>6</ml:real> <ml:real>7</ml:real> <ml:real>8</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="318" left="120" top="1901.25" width="42.75" height="128.25" align-x="132.75" align-y="1968" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Y</ml:id> <ml:matrix rows="8" cols="1"> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>4</ml:real> <ml:real>9</ml:real> <ml:real>24</ml:real> <ml:real>45</ml:real> <ml:real>50</ml:real> <ml:real>80</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="42"/> </region> <region region-id="319" left="18" top="2048.25" width="217.5" height="12" align-x="30" align-y="2058" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> =pentru aproximare, folosim o functie logaritmica: </text> </region> <region region-id="320" left="12" top="2073" width="164.25" height="18" align-x="53.25" align-y="2082" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="logfit">f</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ln</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">z</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="43"/> </region> <region region-id="321" left="186" top="2072.25" width="231.75" height="12" align-x="207.75" align-y="2082" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> coeficientii se exprima cu functia predefinita LOGFIT </text> </region> <region region-id="322" left="24" top="2096.25" width="222.75" height="12" align-x="39" align-y="2106" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> definim coeficientii, dandu-le o valoare (de evitat 0) </text> </region> <region region-id="323" left="30" top="2116.5" width="51" height="45.75" align-x="55.5" align-y="2142" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <ml:matrix rows="3" cols="1"> <ml:real>1</ml:real> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="44"/> </region> <region region-id="324" left="24" top="2168.25" width="69.75" height="12" align-x="38.25" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> =apelam functia </text> </region> <region region-id="325" left="24" top="2181" width="102.75" height="12.75" align-x="49.5" align-y="2190" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <ml:apply> <ml:id xml:space="preserve">logfit</ml:id> <ml:sequence> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">coef</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="326" left="24" top="2197.5" width="100.5" height="63.75" align-x="48" align-y="2232" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">coef</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>29774.768526458975</ml:real> <ml:real>2697.095358179708</ml:real> <ml:real>-235241.22697158987</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="46"/> </region> <region region-id="327" left="18" top="2264.25" width="171" height="12" align-x="30" align-y="2274" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> reprez grafic functia, dupa ce o definim </text> </region> <region region-id="328" left="24" top="2283" width="174" height="18" align-x="66.75" align-y="2292" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="logfit">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">ln</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">z</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">coef</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> 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