009C Sample Midterm 3 - Revision history

Kayla Murray: /* Problem 4 */

2017-11-24T01:55:26Z

Problem 4

Kayla Murray: /* Problem 3 */

2017-11-24T01:55:19Z

Problem 3

Kayla Murray: /* Problem 1 */

2017-11-24T01:55:08Z

Problem 1

Kayla Murray: /* Problem 5 */

2017-11-24T01:42:01Z

Problem 5

Kayla Murray at 01:41, 24 November 2017

2017-11-24T01:41:47Z

Grad: /* Sum of a Series */

2015-04-24T05:55:23Z

Sum of a Series

Grad at 20:14, 23 April 2015

2015-04-23T20:14:30Z

Grad at 20:13, 23 April 2015

2015-04-23T20:13:45Z

Grad at 20:13, 23 April 2015

2015-04-23T20:13:24Z

Grad at 19:54, 23 April 2015

2015-04-23T19:54:38Z

← Older revision		Revision as of 01:55, 24 November 2017
Line 37:		Line 37:

	<span class="exam">(b)  <math>{\displaystyle \sum_{n=1}^{\infty}}\,(-1)^{n}\cos\frac{\pi}{n}</math>		<span class="exam">(b)  <math>{\displaystyle \sum_{n=1}^{\infty}}\,(-1)^{n}\cos\frac{\pi}{n}</math>
−
−

	== [[009C_Sample Midterm 3,_Problem_5\|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] ==		== [[009C_Sample Midterm 3,_Problem_5\|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] ==

← Older revision		Revision as of 01:55, 24 November 2017
Line 30:		Line 30:

	<span class="exam">(b)  <math>{\displaystyle \sum_{n=2}^{\infty}}\,\frac{\sqrt{n}}{n^{2}-3}</math>		<span class="exam">(b)  <math>{\displaystyle \sum_{n=2}^{\infty}}\,\frac{\sqrt{n}}{n^{2}-3}</math>
−

	== [[009C_Sample Midterm 3,_Problem_4\|<span class="biglink"><span style="font-size:80%"> Problem 4 </span>]] ==		== [[009C_Sample Midterm 3,_Problem_4\|<span class="biglink"><span style="font-size:80%"> Problem 4 </span>]] ==

← Older revision		Revision as of 01:55, 24 November 2017
Line 10:		Line 10:

	::<math>a_{n}=\left(\frac{n-7}{n}\right)^{\frac{1}{n}}</math>		::<math>a_{n}=\left(\frac{n-7}{n}\right)^{\frac{1}{n}}</math>
−
−

	== [[009C_Sample Midterm 3,_Problem_2\|<span class="biglink"><span style="font-size:80%"> Problem 2 </span>]] ==		== [[009C_Sample Midterm 3,_Problem_2\|<span class="biglink"><span style="font-size:80%"> Problem 2 </span>]] ==

← Older revision		Revision as of 01:42, 24 November 2017
Line 49:		Line 49:
	<span class="exam">(a)  <math>{\displaystyle \sum_{n=0}^{\infty}}\frac{(-1)^{n}x^{n}}{n+1}</math>		<span class="exam">(a)  <math>{\displaystyle \sum_{n=0}^{\infty}}\frac{(-1)^{n}x^{n}}{n+1}</math>

−	::<span class="exam">(b)  <math>{\displaystyle \sum_{n=0}^{\infty}}\frac{(x+1)^{n}}{n^{2}}</math>	+	<span class="exam">(b)  <math>{\displaystyle \sum_{n=0}^{\infty}}\frac{(x+1)^{n}}{n^{2}}</math>

@@ Line 1: / Line 1: @@
-'''This is a department sample midterm, and is meant to represent the material usually covered in Math 9C through the midterm. Click on the <span class="biglink" style="color:darkblue;">&nbsp;boxed problem numbers&nbsp;</span> to go to a solution.'''
+'''This is a sample, and is meant to represent the material usually covered in Math 9C for the midterm. An actual test may or may not be similar.'''
-'''In-class Instructions:''' This exam has a total of 60 points. You have 50 minutes. You must show all your work to receive full credit You may use any
+'''Click on the''' '''<span class="biglink" style="color:darkblue;">&nbsp;boxed problem numbers&nbsp;</span> to go to a solution.'''
-result done in class. The points attached to each problem are indicated beside the problem.You are not allowed books, notes, or calculators.
+<div class="noautonum">__TOC__</div>
-== Convergence and Limits of a Sequence ==
+<span class="exam">If it converges, also find the limit of the sequence.
-<span class="exam">[[009C_Sample_Midterm_3,_Problem_1|<span class="biglink">&nbsp;Problem 1.&nbsp;</span>]] &nbsp;(12 points) Test if the following sequence <math  style="vertical-align: -10%">{a_n}</math> converges or diverges. If it converges, also find the limit of the sequence.
+::<math>a_{n}=\left(\frac{n-7}{n}\right)^{\frac{1}{n}}</math>
-<span class="exam">[[009C_Sample_Midterm_3,_Problem_2|<span class="biglink">&nbsp;Problem 2.&nbsp;</span>]] &nbsp;For each the following series find the sum, if it converges. If
+== [[009C_Sample Midterm 3,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==
-you think it diverges, explain why.
+<span class="exam">For each the following series find the sum, if it converges.
-::<span class="exam">(a) (6 points) &nbsp;&nbsp;&nbsp;&nbsp; <math style="vertical-align: -50%">\frac{1}{2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3^{2}}-\frac{1}{2\cdot3^{3}}+\frac{1}{2\cdot3^{4}}-\frac{1}{2\cdot3^{5}}+\cdots .</math>
+<span class="exam">If you think it diverges, explain why.
 <br>
-::<span class="exam">(b) (6 points) &nbsp;&nbsp;&nbsp;&nbsp; <math style="vertical-align: -75%"> \sum_{n=1}^{\infty}\,\frac{3}{(2n-1)(2n+1)}.</math>
+<span class="exam">(b) &nbsp;<math style="vertical-align: -75%"> \sum_{n=1}^{\infty}\,\frac{3}{(2n-1)(2n+1)}</math>
-== Convergence Tests for Series I ==
+== [[009C_Sample Midterm 3,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==
-<span class="exam">[[009C_Sample_Midterm_3,_Problem_3|<span class="biglink">&nbsp;Problem 3.&nbsp;</span>]] &nbsp;Test if each the following series converges or diverges. Give reasons
+<span class="exam">Give reasons and clearly state if you are using any standard test.
-::<span class="exam">(a) (6 points) &nbsp;&nbsp;&nbsp;&nbsp; <math>{\displaystyle \sum_{n=1}^{\infty}}\,\frac{n!}{(3n+1)!}.</math>
+<span class="exam">(a) &nbsp;<math>{\displaystyle \sum_{n=1}^{\infty}}\,\frac{n!}{(3n+1)!}</math>
 <br>
-::<span class="exam">(b) (6 points) &nbsp;&nbsp;&nbsp;&nbsp; <math>{\displaystyle \sum_{n=2}^{\infty}}\,\frac{\sqrt{n}}{n^{2}-3}.</math>
+<span class="exam">(b) &nbsp;<math>{\displaystyle \sum_{n=2}^{\infty}}\,\frac{\sqrt{n}}{n^{2}-3}</math>
-== Convergence Tests for Series II ==
+<span class="exam">(a) &nbsp;<math>{\displaystyle \sum_{n=1}^{\infty}}\,(-1)^{n}\sin\frac{\pi}{n}</math>
-::<span class="exam">(a) (6 points) &nbsp;&nbsp;&nbsp;&nbsp; <math>{\displaystyle \sum_{n=1}^{\infty}}\,(-1)^{n}\sin\frac{\pi}{n}.</math>
+<span class="exam">(b) &nbsp;<math>{\displaystyle \sum_{n=1}^{\infty}}\,(-1)^{n}\cos\frac{\pi}{n}</math>
-<span class="exam">[[009C_Sample_Midterm_3,_Problem_5|<span class="biglink">&nbsp;Problem 5.&nbsp;</span>]] &nbsp;Find the radius of convergence and the interval of convergence
+== [[009C_Sample Midterm 3,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==
 of the series.
-::<span class="exam">(a) (6 points) &nbsp;&nbsp;&nbsp;&nbsp; <math>{\displaystyle \sum_{n=0}^{\infty}}\frac{(-1)^{n}x^{n}}{n+1}.</math>
+<span class="exam">(a) &nbsp;<math>{\displaystyle \sum_{n=0}^{\infty}}\frac{(-1)^{n}x^{n}}{n+1}</math>
-::<span class="exam">(b) (6 points) &nbsp;&nbsp;&nbsp;&nbsp; <math>{\displaystyle \sum_{n=0}^{\infty}}\frac{(x+1)^{n}}{n^{2}}.</math>
+::<span class="exam">(b) &nbsp;<math>{\displaystyle \sum_{n=0}^{\infty}}\frac{(x+1)^{n}}{n^{2}}</math>

@@ Line 3: / Line 3: @@
 '''In-class Instructions:''' This exam has a total of 60 points. You have 50 minutes. You must show all your work to receive full credit You may use any
 result done in class. The points attached to each problem are indicated beside the problem.You are not allowed books, notes, or calculators.
-Answers should be written as <math style="vertical-align: -4%">\sqrt{2}</math> as opposed to <math style="vertical-align: -3%">1.4142135\ldots</math>
+Answers should be written as <math style="vertical-align: -5%">\sqrt{2}</math> as opposed to <math style="vertical-align: -3.5%">1.4142135\ldots</math>