Review Test 3
Malgorzata Czerwi ska Math 263
n
1. Find the radius of convergence and interval of convergence of the series.
(a)
n=0
(b)
n=0
(c)
n=1
(d)
n=1
(1)n xn
n+1
xn
n!
3n (x + 4)n
n
(1)n (x 1)n
2n + 1
2. Find the power series representation for the
1
THE TEST FOR DIVERGENCE If lim an does not exist or if
n
lim an = 0, then the series
n
an is divergent.
n=1
THE INTEGRAL TEST Suppose is a continuous, positive, decreasing
function on [1, ) and let an = f (n) . Then the series
n=1
and only if the improp
Practice Test 1
Gosia Czerwi ska Math 263
n
1. Find the area of the surface obtained by rotating the curve x = 3t t3
y = 3t2 , 0 t 1 about the x-axis.
1
2. The curve x = et t y = 4e 2 t , 0 t 1 is rotated about the y-axis.
Find the area of the resulting s
Math 263
Gosia Czerwi ska
n
due 03-22-12
Test 2 Name:
This exam has 5 questions for a total of 100 points. You may earn an extra 10 points
by answering the bonus questions.
Please show your work. Writing down answers with no work may not give you any
cr
Suggested Problems for Test 1
Tentatively, Test 1 consists of 16 problems.
1. 5 problems similar to
Exercises 9, 11, 14, 15, 20, 26, 35, 36, 43, 44
(Section 8.2, page 546).
2. 3 problems similar to
E