Difference between revisions of "009C Sample Final 1, Problem 6"

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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
!Step 1:    
 
!Step 1:    
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|First, we make a table to find the coefficients of the Taylor polynomial.
 
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<table border="1" cellspacing="0" cellpadding="6" align = "center">
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  <tr>
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    <td align = "center"><math> n</math></td>
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    <td align = "center"><math> f^{(n)}(x) </math></td>
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    <td align = "center"><math> f^{(n)}(a) </math></td>
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    <td align = "center"><math> \frac{f^{(n)}(a)}{n!} </math></td>
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  </tr>
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  <tr>
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    <td align = "center"><math>0</math></td>
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    <td align = "center"><math>  </math></td>
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    <td align = "center"><math>  </math></td>
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    <td align = "center"><math> </math></td>
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  </tr>
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<tr>
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    <td align = "center"><math>1</math></td>
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    <td align = "center"><math>  </math></td>
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    <td align = "center"><math>  </math></td>
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    <td align = "center"><math> </math></td>
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  </tr>
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<tr>
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    <td align = "center"><math>2</math></td>
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    <td align = "center"><math>  </math></td>
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    <td align = "center"><math>  </math></td>
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    <td align = "center"><math> </math></td>
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  </tr>
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<tr>
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    <td align = "center"><math>3</math></td>
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    <td align = "center"><math>  </math></td>
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    <td align = "center"><math>  </math></td>
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    <td align = "center"><math> </math></td>
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  </tr>
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<tr>
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    <td align = "center"><math>4</math></td>
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    <td align = "center"><math>  </math></td>
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    <td align = "center"><math>  </math></td>
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    <td align = "center"><math> </math></td>
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  </tr>
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</table>
 
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Revision as of 09:52, 8 February 2016

Find the Taylor polynomial of degree 4 of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)=\cos^2x} at Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a=\frac{\pi}{4}} .

Foundations:  

Solution:

Step 1:  
First, we make a table to find the coefficients of the Taylor polynomial.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f^{(n)}(x) } Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f^{(n)}(a) } Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{f^{(n)}(a)}{n!} }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4}
Step 2:  
Final Answer:  

Return to Sample Exam

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