Calculus II
Exam 3, Spring 2003
Remember : You may use graphing calculators and tables of integrals, but you MUST show that you know
your work.
1. Find the limits
a) lim
tan x x π 2 x π 2
ex 2
b) lim 2x
x ∞ e
2. Does the integral converge or diverge? Give reasons. If you can, evaluate the integral.
∞
dx
a) 2
3 x ln x 1
dx
b) 2
0 x 1
3. Does the series converge or diverge? Give reasons.
∞
e
n
a) ∑ e
n 0 n
∞
3n2 5n 17
b) ∑ 3
n 0 4n 25n 1
∞
5n
c) ∑ 2
1 2
n
n 0
4. What is the radius of convergence of the power series? Show your work.
∞
a) ∑ 5n x 2 n
n 0
∞ x2n 1
b) ∑ 1 n
n!
n 0
5. Find the Maclaurin series for the function. DO a) OR b).
a
1 x
1 4x2
b x
0
e
t2
dt