Name:
ST#
Math 1220-1
Exam 1
Useful Information
1
Dx sin−1 x = √
1 − x2
−1
Dx cos−1 x = √
1 − x2
Dx tan−1 x =
a
1 + x2
Dx sec−1 x =
1
√
|x| x2 − 1
Dx sinh x = cosh x
Dx cosh x = sinh x
cos2 θ + sin2 θ = 1
sin2 x =
1 − cos 2x
2
cos2 x =
1 + cos 2x
2
sin 2θ = 2 sin θ cos θ
1
Math 1220-1
Exam 1
Directions: Show all work. Write your answer in the space provided. Please
box your answer.
√
1. (5 pts) Find f ′ (9) if f (x) = ln x.
2. (8 pts) Find
Z
2
xex
2
−4
dx.
1
2
3. (9 pts) If f (x) = xsin x , find f ′ (π).
4. (10 pts) The Galileo spacecraft entered the atmosphere at a record temperature of 14, 000◦C. If the spacecraft were to land in the Salt Flats
in January in 5◦ C weather, the differential equation for Newton’s Law of
Cooling gives us that
dT
= k(T − 5),
dt
where k is a constants. Solve this differential equation. (Note: k will be
in your answer.)
3
2
5. (10 pts) Solve y ′ + 2xy = xe−x .
6. (7 pts) Find
Z
√
x x − 1 dx.
4
7. (8 pts) Find
Z
x sinh x dx.
8. (8 pts) Give the partial fraction decomposition for
5
3x − 13
.
x2 + 3x − 10