Review Test 3
Malgorzata Czerwi ska Math 263
1. Find the radius of convergence and interval of convergence of the series.
3n (x + 4)n
(1)n (x 1)n
2n + 1
2. Find the power series representation for the
THE TEST FOR DIVERGENCE If lim an does not exist or if
lim an = 0, then the series
an is divergent.
THE INTEGRAL TEST Suppose is a continuous, positive, decreasing
function on [1, ) and let an = f (n) . Then the series
and only if the improp
Practice Test 1
Gosia Czerwi ska Math 263
1. Find the area of the surface obtained by rotating the curve x = 3t t3
y = 3t2 , 0 t 1 about the x-axis.
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
Gosia Czerwi ska
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