009C Sample Final 3 - Revision history

Kayla Murray: /* Problem 9 */

2017-12-03T23:35:06Z

Problem 9

2017-12-03T23:29:57Z

Problem 8

2017-12-03T23:25:10Z

Problem 7

2017-12-03T23:21:01Z

Problem 6

2017-12-03T23:20:45Z

Problem 5

2017-03-17T21:50:03Z

Problem 6

2017-03-12T20:56:20Z

Problem 4

2017-03-05T01:24:27Z

Problem 10

2017-03-05T01:23:37Z

Problem 9

2017-03-05T01:22:46Z

Problem 9

@@ Line 82: / Line 82: @@
 == [[009C_Sample Final 3,_Problem_9|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 9&nbsp;</span>]] ==
-<span class="exam">A wheel of radius 1 rolls along a straight line, say the &nbsp;<math>x</math>-axis. A point &nbsp;<math style="vertical-align: 0px">P</math>&nbsp; is located halfway between the center of the wheel and the rim. As the wheel rolls, &nbsp;<math style="vertical-align: 0px">P</math>&nbsp; traces a curve. Find parametric equations for the curve.
+<span class="exam">A wheel of radius 1 rolls along a straight line, say the &nbsp;<math>x</math>-axis. A point &nbsp;<math style="vertical-align: 0px">P</math>&nbsp; is located halfway between the center of the wheel and the rim; assume &nbsp;<math style="vertical-align: 0px">P</math>&nbsp; starts at the point &nbsp;<math style="vertical-align: -15px">\bigg(0,\frac{1}{2}\bigg).</math>&nbsp; As the wheel rolls, &nbsp;<math style="vertical-align: 0px">P</math>&nbsp; traces a curve. Find parametric equations for the curve.
 == [[009C_Sample Final 3,_Problem_10|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 10&nbsp;</span>]] ==

@@ Line 74: / Line 74: @@
 == [[009C_Sample Final 3,_Problem_8|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 8&nbsp;</span>]] ==
-<span class="exam">A curve is given in polar coordinates by &nbsp;<math style="vertical-align: -2px">r=4+3\sin \theta</math>
+<span class="exam">A curve is given in polar coordinates by &nbsp;<math style="vertical-align: -2px">r=4+3\sin \theta.</math>
 <span class="exam">(a) Sketch the curve.

@@ Line 64: / Line 64: @@
 <span class="exam">A curve is given in polar coordinates by
-::<math>r=1+\cos^2(2\theta)</math>
+::<math>r=1+\cos^2(2\theta).</math>
 <span class="exam">(a) Show that the point with Cartesian coordinates &nbsp;<math style="vertical-align: -15px">(x,y)=\bigg(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\bigg)</math>&nbsp; belongs to the curve.

@@ Line 46: / Line 46: @@
 <span class="exam"> Consider the power series
-::<math>\sum_{n=0}^\infty (-1)^n \frac{x^{n+1}}{n+1}</math>
+::<math>\sum_{n=0}^\infty (-1)^n \frac{x^{n+1}}{n+1}.</math>
 <span class="exam">(a) Find the radius of convergence of the above power series.

@@ Line 35: / Line 35: @@
 <span class="exam"> Consider the function
-::<math>f(x)=e^{-\frac{1}{3}x}</math>
+::<math>f(x)=e^{-\frac{1}{3}x}.</math>
 <span class="exam">(a) Find a formula for the &nbsp;<math>n</math>th derivative &nbsp;<math style="vertical-align: -5px">f^{(n)}(x)</math>&nbsp; of &nbsp;<math style="vertical-align: -5px">f</math>&nbsp; and then find &nbsp;<math style="vertical-align: -5px">f'(3).</math>

@@ Line 58: / Line 58: @@
 ::<math>\sum_{n=0}^\infty \frac{1}{(n+1)3^{n+1}}</math>
-<span class="exam">converge? If so, find its sum.
+<span class="exam">converge?
 == [[009C_Sample Final 3,_Problem_7|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 7&nbsp;</span>]] ==

@@ Line 28: / Line 28: @@
 <span class="exam"> Determine if the following series converges or diverges. Please give your reason(s).
-<span class="exam">(a) &nbsp;<math>\sum_{n=1}^{+\infty} \frac{n!}{(2n)!}</math>
+<span class="exam">(a) &nbsp;<math>\sum_{n=1}^{\infty} \frac{n!}{(2n)!}</math>
-<span class="exam">(b) &nbsp;<math>\sum_{n=1}^{+\infty} (-1)^n\frac{1}{n+1}</math>
+<span class="exam">(b) &nbsp;<math>\sum_{n=1}^{\infty} (-1)^n\frac{1}{n+1}</math>
 == [[009C_Sample Final 3,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==

@@ Line 91: / Line 91: @@
 ::<span class="exam"><math>y=t^3-t</math>
-<span class="exam">(a) Sketch the curve for &nbsp;<math>-2\le t \le 2.</math>
+<span class="exam">(a) Sketch the curve for &nbsp;<math style="vertical-align: -2px">-2\le t \le 2.</math>
 <span class="exam">(b) Find the equation of the tangent line to the curve at the origin.

@@ Line 83: / Line 83: @@
 == [[009C_Sample Final 3,_Problem_9|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 9&nbsp;</span>]] ==
-<span class="exam">A wheel of radius 1 rolls along a straight line, say the <math>x</math>-axis. A point <math>P</math> is located halfway between the center of the wheel and the rim. As the wheel rolls, <math>P</math> traces a curve. Find parametric equations for the curve.
+<span class="exam">A wheel of radius 1 rolls along a straight line, say the <math>x</math>-axis. A point <math style="vertical-align: 0px">P</math> is located halfway between the center of the wheel and the rim. As the wheel rolls, <math style="vertical-align: 0px">P</math> traces a curve. Find parametric equations for the curve.
 == [[009C_Sample Final 3,_Problem_10|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 10&nbsp;</span>]] ==