MA140
2/23/09
Major Quiz 3 Review Problems
1.) Find an equation of the tangent line to the graph of the cosine function at the point
where x =
4
π
.
2.) Find each of the following.
(a)
5
2
sec
2cotcsc
+
x
xx
dx
d (b)
+
xx
x
dx
d
cos
sin1 (c)
+2
2
1
sec
x
x
dx
d
(d)
10
2
csc1
)2sin(
+
+
x
x
dx
d (e)
(
)
1354 )6()( −− −− xxx
dx
d
(f)
(
)
xx
dx
dsectan 3 (g)
(
)
(
)
10023 )(cot)2(csc xx
dx
d+
3.) Find
dx
dy for each of the following.
(a)
x
x
y
3 2 5+
= (b) 5)42tan()2sin(
=
−
−
+
yxyx
4.) Find the equation of the tangent line to the curve x2y − 3y = y3 at (2,1).
5.) A boy five feet tall walks at a rate of 168 feet per minute on a straight horizontal
path away from a light that hangs twelve feet above the path. How fast does his shadow
lengthen?
6.) Every day, a flight from Los Angeles to New York flies directly over my home at a
constant altitude of 4 miles. If I assume that the plane is flying at a constant speed of 400
mi/h, at what rate is the angle of elevation of my line of sight changing with respect to time
when the horizontal distance between the approaching plane and my location is exactly 3
miles?
7.) Find
dx
dy for each of the following.
(a) 4x2 + 3y2 = 1 (b) x = sin (x + y)
8.) Find an equation of the tangent line to the curve 9x3 - y3 = 1 at the point (1,2).
9.) Find
+2
2
1
sec
x
x
dx
d.
