Math 126
Carter
Test 2
Spring 2011
General Instructions: Write your name on only the outside of your blue book. Do all
of your work and write your answers inside your blue book. Put your test paper inside your
blue book as you leave. Solve each of the following problems; point values are indicated on
the problems. There are 105 total points available on the test. Please yield the right of way
to pedestrians and bicycles.
1. (8 points each) Compute the following:
Z
(a)
Z
(b)
x2
Z
(c)
Z
(d)
(e)
ln (x) dx
1
dx
+9
e2x cos (x) dx
√
9 − x2 dx
1
dx
(x − 2)(x − 1)
Z
Z ∞
(f)
1
dx
x2
2. (7 points) Define
lim an = L.
n→∞
Rbq
3. (10 points) Compute the arc length (
a
1 + (f 0 (x))2 dx) of f (x) = 3x+1 for x ∈ [0, 3].
4. (10 points) Compute
√ the volume of the solid obtained by rotating the region bounded
by y = x2 and y = x about the x-axis.
5. (10 points) Assuming a spring constant of k = 600kg/sec2 , compute the work in Joules
(kilogram meter-squared per second-squared) that is required to stretch the spring 10
centimeters beyond equilibrium.
6. (10 points) Compute the work needed in building a brick (density 80 pounds per cubicfoot) structure that is a tower of height 10 feet and square base of side 20 feet.
7. (10 points) Compute the (Taylor) MacLaurin polynomial T5 (x) =
of the indicated function at the point a.
f (x) = ln (x + 1); a = 0.
1
P5
j=0
f (j) (a)
(x
j!
− a)j