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
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
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 rot
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. Wr
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