009C Sample Final 1, Problem 6 - Revision history

Kayla Murray at 01:08, 3 December 2017

2017-12-03T01:08:27Z

2017-02-26T23:24:52Z

2017-02-26T23:17:59Z

2017-02-26T00:05:35Z

2016-04-19T01:36:25Z

2016-03-01T18:44:58Z

2016-02-29T18:38:37Z

2016-02-23T23:04:29Z

2016-02-22T20:51:14Z

2016-02-22T20:49:45Z

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

← Older revision		Revision as of 23:24, 26 February 2017
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−	<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>.	+	<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>.

	{\| class="mw-collapsible mw-collapsed" style = "text-align:left;"		{\| class="mw-collapsible mw-collapsed" style = "text-align:left;"

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 !Foundations: &nbsp;
 |-
-|The Taylor polynomial of <math style="vertical-align: -5px">f(x)</math> at <math style="vertical-align: -1px">a</math> is
+|The Taylor polynomial of  &nbsp; <math style="vertical-align: -5px">f(x)</math> &nbsp; at &nbsp; <math style="vertical-align: -1px">a</math> &nbsp; is
 |-
+|
@@ Line 62: / Line 62: @@
 !Step 2: &nbsp;
 |-
-|Since <math style="vertical-align: -14px">c_n=\frac{f^{(n)}(a)}{n!},</math> the Taylor polynomial of degree 4 of <math style="vertical-align: -5px">f(x)=\cos^2x</math> is
+|Since &nbsp; <math style="vertical-align: -14px">c_n=\frac{f^{(n)}(a)}{n!},</math>&nbsp; the Taylor polynomial of degree 4 of &nbsp;<math style="vertical-align: -5px">f(x)=\cos^2x</math>&nbsp; is
+|
 |-

@@ Line 7: / Line 7: @@
 |-
+|
-::<math>\sum_{n=0}^{\infty}c_n(x-a)^n</math> where <math style="vertical-align: -14px">c_n=\frac{f^{(n)}(a)}{n!}.</math>
+&nbsp; &nbsp; &nbsp; &nbsp;<math>\sum_{n=0}^{\infty}c_n(x-a)^n</math> where <math style="vertical-align: -14px">c_n=\frac{f^{(n)}(a)}{n!}.</math>
 |}
 '''Solution:'''
@@ Line 65: / Line 66: @@
 |-
+|
-::<math>T_4(x)=\frac{1}{2}+-1\bigg(x-\frac{\pi}{4}\bigg)+\frac{2}{3}\bigg(x-\frac{\pi}{4}\bigg)^3.</math>
+&nbsp; &nbsp; &nbsp; &nbsp;<math>T_4(x)=\frac{1}{2}+-1\bigg(x-\frac{\pi}{4}\bigg)+\frac{2}{3}\bigg(x-\frac{\pi}{4}\bigg)^3.</math>
 |}
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Final Answer: &nbsp;
 |-
-|&nbsp;&nbsp; <math>\frac{1}{2}+-1\bigg(x-\frac{\pi}{4}\bigg)+\frac{2}{3}\bigg(x-\frac{\pi}{4}\bigg)^3</math>
+|&nbsp; &nbsp; &nbsp; &nbsp; <math>\frac{1}{2}+-1\bigg(x-\frac{\pi}{4}\bigg)+\frac{2}{3}\bigg(x-\frac{\pi}{4}\bigg)^3</math>
 |}
 [[009C_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]

@@ Line 71: / Line 71: @@
 !Final Answer: &nbsp;
 |-
-|<math>\frac{1}{2}+-1\bigg(x-\frac{\pi}{4}\bigg)+\frac{2}{3}\bigg(x-\frac{\pi}{4}\bigg)^3</math>
+|&nbsp;&nbsp; <math>\frac{1}{2}+-1\bigg(x-\frac{\pi}{4}\bigg)+\frac{2}{3}\bigg(x-\frac{\pi}{4}\bigg)^3</math>
 |}
 [[009C_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]

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 |-
+|
-::<math>T_4(x)=\frac{1}{2}+-1\bigg(x-\frac{\pi}{4}\bigg)+\frac{2}{3}\bigg(x-\frac{\pi}{4}\bigg)^3</math>.
+::<math>T_4(x)=\frac{1}{2}+-1\bigg(x-\frac{\pi}{4}\bigg)+\frac{2}{3}\bigg(x-\frac{\pi}{4}\bigg)^3.</math>
 |}

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 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Foundations: &nbsp;
 |-
+|
 |}
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    </tr>
 </table>
 |}

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 !Step 2: &nbsp;
 |-
-|Since <math>c_n=\frac{f^{(n)}(a)}{n!} </math>, the Taylor polynomial of degree 4 of <math>f(x)=\cos^2x</math> is
+|Since <math style="vertical-align: -14px">c_n=\frac{f^{(n)}(a)}{n!} </math>, the Taylor polynomial of degree 4 of <math style="vertical-align: -5px">f(x)=\cos^2x</math> is
+|
 |-
 |<math>T_4(x)=\frac{1}{2}+-1\bigg(x-\frac{\pi}{4}\bigg)+\frac{2}{3}\bigg(x-\frac{\pi}{4}\bigg)^3</math>.
 |}
@@ Line 73: / Line 74: @@
 !Final Answer: &nbsp;
 |-
-|<math>T_4(x)=\frac{1}{2}+-1\bigg(x-\frac{\pi}{4}\bigg)+\frac{2}{3}\bigg(x-\frac{\pi}{4}\bigg)^3</math>
+|<math>\frac{1}{2}+-1\bigg(x-\frac{\pi}{4}\bigg)+\frac{2}{3}\bigg(x-\frac{\pi}{4}\bigg)^3</math>
 |}
 [[009C_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]

← Older revision		Revision as of 20:49, 22 February 2016
Line 1:		Line 1:
−	<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>.

	{\| class="mw-collapsible mw-collapsed" style = "text-align:left;"		{\| class="mw-collapsible mw-collapsed" style = "text-align:left;"