Math 30
Exam 2 (Section 3.1 – 3.9)
Spring 2009
Practice Problems
1. A stone is thrown vertically upward from the surface of the moon with a
velocity of 10 m/sec. Its height (in meters) after t seconds is given by
2
5
() 10 6
t
ht t=−.
a. What is the velocity of the stone after 3 seconds?
b. What is the maximum height reached by the stone?
c. When does the stone hit the surface of the moon?
For problems 2 – 7, find the derivative dy
ydx
′= and simplify.
2.
44 ln( ) log
xx
yx e e x x
ππ
π
=++++ +
3.
()
tan
sin x
yx=
4. arctan(arcsin )yx=
5.
()
()
34
25
2
52
3
sin 2 1
31 2
x
exx
yxx
+
=
−+
6. sin3
x
y
x
=
7. 12
tan ln 1yx x x
−
=−+
8. Evaluate
()
4
4
0
lim tan 3
x
x
x
→
9. If
(3 , ,
) 4f=(3) 2g=(3) 6f′
=
−, and (3) 5g
′
=
, evaluate the following :
a.
()
b.
(3)fg ′
(
)
()
3
fg
′
