009C Sample Final 2, Problem 5 - Revision history

Kayla Murray at 01:29, 3 December 2017

2017-12-03T01:29:23Z

2017-03-11T00:21:54Z

2017-03-11T00:11:38Z

2017-03-05T02:21:09Z

2017-03-05T01:14:29Z

2017-03-05T00:48:25Z

2017-03-05T00:41:54Z

2017-02-18T18:18:29Z

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 <span class="exam"> Find the Taylor Polynomials of order 0, 1, 2, 3 generated by &nbsp;<math style="vertical-align: -5px">f(x)=\cos(x)</math>&nbsp; at &nbsp;<math style="vertical-align: -14px">x=\frac{\pi}{4}.</math>
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+<hr>
-!Foundations: &nbsp;
+[[009C Sample Final 2, Problem 5 Solution|'''<u>Solution</u>''']]
-'''Solution:'''
+[[009C Sample Final 2, Problem 5 Detailed Solution|'''<u>Detailed Solution</u>''']]
 [[009C_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]

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 |-
 |Since &nbsp; <math style="vertical-align: -14px">c_n=\frac{f^{(n)}(a)}{n!},</math>&nbsp; we have
 |-
 |&nbsp; &nbsp; &nbsp; &nbsp;<math>T_0=\frac{\sqrt{2}}{2}</math>

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 |-
+|
-<table border="1" cellspacing="0" cellpadding="6" align = "center">
+<table border="1" cellspacing="0" cellpadding="11" align = "center">
    <tr>
      <td align = "center"><math> n</math></td>
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 |-
 |&nbsp; &nbsp; &nbsp; &nbsp;Let &nbsp;<math style="vertical-align: -4px">T_n</math>&nbsp; be the Taylor polynomial of order &nbsp;<math>n.</math>
 |-
 |&nbsp; &nbsp; &nbsp; &nbsp;<math>T_0=\frac{\sqrt{2}}{2}</math>

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 !Foundations: &nbsp;
 |-
+|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
 |-
+|
 |}
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 !Step 1: &nbsp;
 |-
+|Let &nbsp;<math style="vertical-align: -14px">a=\frac{\pi}{4}.</math>
 |-
+|First, we make a table to find the coefficients of the Taylor polynomial.
 |-
+|
 |}
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 !Step 2: &nbsp;
 |-
+|Let &nbsp;<math style="vertical-align: -4px">T_n</math>&nbsp; be the Taylor polynomial of order &nbsp;<math>n.</math>
 |-
 |}
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 !Final Answer: &nbsp;
 |-
-|&nbsp;&nbsp;
+|&nbsp; &nbsp; &nbsp; &nbsp;Let &nbsp;<math style="vertical-align: -4px">T_n</math>&nbsp; be the Taylor polynomial of order &nbsp;<math>n.</math>
 |}
 [[009C_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]

← Older revision		Revision as of 01:14, 5 March 2017
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−	<span class="exam"> Find the Taylor Polynomials of order 0, 1, 2, 3 generated by  <math>f(x)=\cos(x)</math>  at  <math>x=\frac{\pi}{4}.</math>	+	<span class="exam"> Find the Taylor Polynomials of order 0, 1, 2, 3 generated by  <math style="vertical-align: -5px">f(x)=\cos(x)</math>  at  <math style="vertical-align: -14px">x=\frac{\pi}{4}.</math>

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← Older revision		Revision as of 00:41, 5 March 2017
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−	<span class="exam"> Find the Taylor Polynomials of order 0, 1, 2, 3 generated by <math>f(x)=\cos(x)</math> at <math>x=\frac{\pi}{4}.</math>	+	<span class="exam"> Find the Taylor Polynomials of order 0, 1, 2, 3 generated by  <math>f(x)=\cos(x)</math>  at  <math>x=\frac{\pi}{4}.</math>

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← Older revision		Revision as of 18:18, 18 February 2017
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−	<span class="exam">~~Compute~~	+	<span class="exam"> Find the Taylor Polynomials of order 0, 1, 2, 3 generated by <math>f(x)=\cos(x)</math> at <math>x=\frac{\pi}{4}.</math>
−
−	::<~~span class="exam"~~>a) ~~<math style~~=~~"vertical-align: -12px">~~\~~lim_{n\rightarrow \infty} \frac{3-2n^2}{5n^2+n+1}~~</math>
−
−	::<~~span class="exam"~~>~~b) <math style~~=~~"vertical-align: -12px">\lim_{n\rightarrow \infty}~~ \frac{\~~ln n~~}{~~\ln 3n~~}</math>

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