Test2 - meters above the ground(Assume the balloon rises...

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Exam #2 - Chapter 3
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1. Sketch the derivatives:
(5 points each)
a.
b.

2.
(10 points each)
Find
dy
dx
for each of the following:
a)
( 29 ( 29
x x y sin sin =
b)
2 2 3 3
y x y x = +

c)
x
x y
1
=
d)
2
3
x
y
x
=

3.
(10 points)
A particle’s position at time t is given by the function
3 2
( ) 12 36 s t t t t = - + for 0 t ≥
a. Find all times when the particle is moving in the positive direction and is slowing down.
b. Find all times when the particle is moving in the negative direction and speeding up.
4.
(10 pts.)
A balloon rises at a rate of 3 meters per second from a point on the ground 30 meters from an observer.
Find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 30