Math 1220-2
Final Exam
Name:
ST#
Show all work. Write your answer in the space provided. Please box your answer. You
may use one piece of paper of notes, but it must be handed in with your test. You may not
use a calculator.
Possibly useful equations:
p
p
p
p
(1 + x) = 1 +
x+
x2 +
x3 + · · ·
1
2
3
p
k
=
p(p − 1)(p − 2) · · · (p − k + 1)
k!
sin2 x =
1 − cos 2x
2
cos2 x =
1 + cos 2x
2
Z
sec θdθ = ln | sec θ + tan θ| + C
Z
csc θdθ = ln | csc θ − cot θ| + C
Math 1220-2
1. (5pts) Find
3
dz
if z = y 2 e5y −ln y
dy
2. (5pts) Find
Z
e−1/x
dx.
x2
3. (10pts) Do either a or b.
1
p
dx
7 − (x + 2)2
Z
3x − 13
(b) Find
dx.
x2 + 3x − 10
(a) Find
Z
Final Exam
4. (6pts) Give a series representation for (1 + x3 )1/7 .
5. (10pts) What is lim (1 + h)1/h ?
h→0
6. (10pts) Evaluate
Z
0
4
x
dx.
ex
7. (10pts) What should cos θ and sin θ be to put the equation 11x2 + 96xy + 39y 2 + 240x + 570y + 875 = 0
into standard form?
8. (10pts) Find the area of the region outside the circle r = 1 and inside the four petal rose r = 2 cos 2θ.
9. (10pts) Solve the following differential equation by using the method of undetermined coefficients:
y ′′ + 3y ′ + 2y = 3e−2x
.
10. (14pts) Solve the following differential equation by using the method of variation of parameters:
y ′′ + y = cot x
.