Mathcad Professional 14.0 <description/> <author>K312-02</author> <company>Parametric Technology Corporation</company> <keywords/> <revisedBy>Fejér Tamás</revisedBy> </userData> <identityInfo> <revision>3</revision> <documentID>6949FB0C-3B89-467D-8705-6029FF83EF31</documentID> <versionID>B9272084-FA29-4E00-B87A-0FB08C67823C</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="14" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 2"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="12" font-weight="bold" font-style="italic" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 3"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Paragraph"> <blockAttr margin-left="0" margin-right="0" text-indent="21" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="List"> <blockAttr margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Indent"> <blockAttr margin-left="108" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Subtitle" base-style="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="large" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variables" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Constants" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 1" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 2" font-family="Courier New" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 3" font-family="Arial" font-charset="0" font-size="10" font-weight="bold" font-style="normal" underline="false"/> <mathStyle name="User 4" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="italic" underline="false"/> <mathStyle name="User 5" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 6" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="Times New Roman" font-charset="0" font-size="14" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="current" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance" display="false"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="9" orientation="portrait" print-single-page-width="false" page-width="595.5" page-height="841.5"> <margins left="86.4" right="86.4" top="86.4" bottom="86.4"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="en" UI="en"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="true" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC12" local-assignment="MC12"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="cm"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="false" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="162" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="139" left="18" top="26.25" width="188.25" height="12" align-x="36" align-y="36" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Vegyünk fel véletlenszerű pontokat a síkon:</p> </text> </region> <region region-id="142" left="240" top="18.75" width="98.25" height="29.25" align-x="252" align-y="36" 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">P</ml:id> <ml:matrix rows="2" cols="5"> <ml:real>2</ml:real> <ml:real>-4</ml:real> <ml:real>1</ml:real> <ml:real>5</ml:real> <ml:real>-6</ml:real> <ml:real>8</ml:real> <ml:real>4</ml:real> <ml:real>9</ml:real> <ml:real>-3</ml:real> <ml:real>3</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="18" left="24" top="102" width="382.5" height="318" align-x="24" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="3"/> <rendering item-idref="4"/> </region> <region region-id="145" left="24" top="494.25" width="159.75" height="12" align-x="39" align-y="504" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Lineáris interpoláció a pontok között:</p> </text> </region> <region region-id="143" left="30" top="528" width="243" height="78.75" align-x="53.25" align-y="570" 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">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:id xml:space="preserve">linterp</ml:id> <ml:sequence> <ml:apply> <ml:matcol/> <ml:parens> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve">P</ml:id> </ml:apply> </ml:parens> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:matcol/> <ml:parens> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve">P</ml:id> </ml:apply> </ml:parens> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:sequence> </ml:apply> <ml:symResult> <ml:apply> <ml:id xml:space="preserve">linterp</ml:id> <ml:sequence> <ml:matrix rows="5" cols="1"> <ml:real>2</ml:real> <ml:real>1</ml:real> <ml:real>-6</ml:real> <ml:real>4</ml:real> <ml:real>-3</ml:real> </ml:matrix> <ml:matrix rows="5" cols="1"> <ml:real>-4</ml:real> <ml:real>5</ml:real> <ml:real>8</ml:real> <ml:real>9</ml:real> <ml:real>3</ml:real> </ml:matrix> <ml:id xml:space="preserve">x</ml:id> </ml:sequence> </ml:apply> </ml:symResult> </ml:symEval> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="33" left="36" top="636" width="38.25" height="78.75" align-x="48.75" align-y="678" 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">T</ml:id> <ml:matrix rows="5" 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:matrix> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="42" left="132" top="675" width="57" height="12.75" align-x="141.75" align-y="684" 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">t</ml:id> <ml:range> <ml:sequence> <ml:real>0.5</ml:real> <ml:real>1</ml:real> </ml:sequence> <ml:real>5.5</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="31" left="30" top="754.5" width="109.5" height="23.25" align-x="51" align-y="774" 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">x</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">linterp</ml:id> <ml:sequence> <ml:id xml:space="preserve">T</ml:id> <ml:apply> <ml:matcol/> <ml:parens> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve">P</ml:id> </ml:apply> </ml:parens> <ml:real>0</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="32" left="30" top="778.5" width="111" height="23.25" align-x="52.5" align-y="798" 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">y</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">linterp</ml:id> <ml:sequence> <ml:id xml:space="preserve">T</ml:id> <ml:apply> <ml:matcol/> <ml:parens> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve">P</ml:id> </ml:apply> </ml:parens> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="150" left="24" top="818.25" width="365.25" height="13.5" align-x="27" align-y="828" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">A <region region-id="149" left="33.75" top="819" width="31.5" height="12.75" align-x="45.75" align-y="828" 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">k</ml:id> <ml:real>3.5</ml:real> </ml:define> </math> <rendering item-idref="10"/> </region> paraméterértékhez tartozó pont a 3. és a 4. pont szakaszfelező pontja.</p> </text> </region> <region region-id="34" left="42" top="918" width="322.5" height="264" align-x="42" align-y="918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="11"/> <rendering item-idref="12"/> </region> <region region-id="152" left="18" top="1250.25" width="79.5" height="12" align-x="30" align-y="1260" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Spline interpoláció</p> </text> </region> <region region-id="51" left="216" top="1299" width="50.25" height="12.75" align-x="225.75" align-y="1308" 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">t</ml:id> <ml:range> <ml:sequence> <ml:real>1</ml:real> <ml:real>1.1</ml:real> </ml:sequence> <ml:real>5</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="47" left="24" top="1354.5" width="189.75" height="27" align-x="49.5" align-y="1374" 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="s">x</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">interp</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">lspline</ml:id> <ml:sequence> <ml:id xml:space="preserve">T</ml:id> 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xml:space="preserve">interp</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">lspline</ml:id> <ml:sequence> <ml:id xml:space="preserve">T</ml:id> <ml:apply> <ml:matcol/> <ml:parens> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve">P</ml:id> </ml:apply> </ml:parens> <ml:real>1</ml:real> </ml:apply> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:apply> <ml:matcol/> <ml:parens> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve">P</ml:id> </ml:apply> </ml:parens> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="50" left="60" top="1476" width="318" height="267.75" align-x="60" align-y="1476" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="16"/> <rendering item-idref="17"/> </region> <region region-id="154" left="18" top="1778.25" width="405" height="24" align-x="33.75" align-y="1788" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Polinom interpoláció: 5 pont esetén n=5-1-ed fokú polinom átmegy a kontrolpontokon, kisebb fokszámú polinom csak közelíti.</p> </text> </region> <region region-id="59" left="252" top="1809" width="24.75" height="12.75" align-x="264" align-y="1818" 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">n</ml:id> <ml:real>4</ml:real> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="52" left="42" top="1828.5" width="203.25" height="27" align-x="67.5" align-y="1848" 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="f">x</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">interp</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">regress</ml:id> <ml:sequence> <ml:id xml:space="preserve">T</ml:id> <ml:apply> <ml:matcol/> <ml:parens> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve">P</ml:id> </ml:apply> </ml:parens> <ml:real>0</ml:real> </ml:apply> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:apply> <ml:matcol/> <ml:parens> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve">P</ml:id> </ml:apply> </ml:parens> <ml:real>0</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="53" left="42" top="1858.5" width="204.75" height="27" align-x="69" align-y="1878" 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="f">y</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">interp</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">regress</ml:id> <ml:sequence> <ml:id xml:space="preserve">T</ml:id> <ml:apply> <ml:matcol/> <ml:parens> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve">P</ml:id> </ml:apply> </ml:parens> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">n</ml:id> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:apply> <ml:matcol/> <ml:parens> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve">P</ml:id> </ml:apply> </ml:parens> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="56" left="42" top="2034" width="318" height="267.75" align-x="42" align-y="2034" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="21"/> <rendering item-idref="22"/> </region> <region region-id="157" left="12" top="2330.25" width="314.25" height="12" align-x="30" align-y="2340" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Vegyünk fel 20 pontot ahol az x koordináták növekvő sorrendben vannak.</p> </text> </region> <region region-id="155" left="18" top="2361" width="31.5" height="12.75" align-x="32.25" align-y="2370" 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">N</ml:id> <ml:real>20</ml:real> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="84" left="60" top="2361" width="36.75" height="12.75" align-x="69" align-y="2370" 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 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<ml:real>116.7838143138215</ml:real> <ml:real>90</ml:real> <ml:real>189.82673982158303</ml:real> <ml:real>95</ml:real> <ml:real>152.75553076062352</ml:real> <ml:real>100</ml:real> <ml:real>187.42600346915424</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="27"/> </resultFormat> </math> <rendering item-idref="28"/> </region> <region region-id="159" left="24" top="2594.25" width="246.75" height="12" align-x="45" align-y="2604" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Közelítsük az alábbi függvények lineáris kombinációjával:</p> </text> </region> <region region-id="107" left="48" top="2630.25" width="52.5" height="74.25" align-x="71.25" align-y="2670" show-border="false" 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top="3012" width="321" height="258" align-x="48" align-y="3012" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="34"/> <rendering item-idref="35"/> </region> <region region-id="161" left="18" top="3313.5" width="382.5" height="28.5" align-x="28.5" align-y="3330" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Most közelítsük a <region region-id="162" left="98.25" top="3314.25" width="50.25" height="27.75" align-x="111.75" align-y="3330" 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:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">l</ml:id> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="36"/> </region> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> függvények kombinációjával, ahol </inlineAttr> </f> <f family="Times New Roman" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">l</inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> az intervallum hossza.</inlineAttr> </f> </p> </text> </region> <region region-id="121" left="42" top="3368.25" 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