APPM 1345 Exam 2 Spring 2011
INSTRUCTIONS: Books, notes, and electronic devices are not permitted. Write (1) your name,
(2) section number, and (3) a grading table on the front of your bluebook. Start each problem on
a new page. Simplify your answers. A correct answer with incorrect or no supporting work may
receive no credit, while an incorrect answer with relevant work may receive partial credit. Unless
otherwise indicated, show all work.
1. (10 points) Solve for x.
(a) x= log82 + log 1
28
(b) x= log23·log34·log48
(c) xlogx10 −2 logx√x= 72 log7x
2. (30 points) Evaluate the following integrals.
(a) Z10t(2 −t2)2/3dt
(b) Zsin 2θcos22θ dθ
(c) Z3
0
x2
√x3+ 9 dx
(d) Z4π2
π2
sin √x
√xdx
3. (10 points)
�2
�1
1
2
3
4
5
6
t
�1
1
y
y�f�t�
Consider the function y=f(t)shown above. Let g(x) = Zx
−2
f(t)dt.
(a) Find g(0).
(b) Find g(2).
(c) At what value(s) of xdoes ghave local maxima?
(d) At what value of xdoes ghave an absolute minimum?
4. (10 points) Differentiate the following functions.
(a) f(x) = Zx
0t4
4−3dt
(b) g(x) = 8 + Zx4
1
2t2+ 1
t3−1dt
(c) h(x) = x2−Zπ/2
1/x
csc tcot t dt
