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| − | <span class="exam"> Find the Taylor polynomial of degree 4 of <math>f(x)=\cos^2x</math> at <math>a=\frac{\pi}{4}</math>. | + | <span class="exam"> Find the Taylor polynomial of degree 4 of <math style="vertical-align: -5px">f(x)=\cos^2x</math> at <math>a=\frac{\pi}{4}</math>. |
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| − | {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
| + | <hr> |
| − | !Foundations:
| + | [[009C Sample Final 1, Problem 6 Solution|'''<u>Solution</u>''']] |
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| − | '''Solution:'''
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| − | {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
| + | [[009C Sample Final 1, Problem 6 Detailed Solution|'''<u>Detailed Solution</u>''']] |
| − | !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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| − | {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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| − | !Step 2:
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| − | |}
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| − | {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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| − | !Final Answer:
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| − | |}
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| | [[009C_Sample_Final_1|'''<u>Return to Sample Exam</u>''']] | | [[009C_Sample_Final_1|'''<u>Return to Sample Exam</u>''']] |
