Math 16B, Section 1
Fall 2005
Sarason
REVIEW EXERCISES 2
1. Perform the differentiations. (a)
d
dt
(sin(ln
t
))
(b)
d
dt
(ln(sin
t
))
(c)
d
dt
(sec(
e
t
))
(d)
d
dt
(tan(sec
t
))
2. Evaluate the integrals. (a)
e
1
ln
x
√
x
dx
(b)
π/
2
0
x
2
cos
x dx
(c)
π/
2
0
cos
3
x
sin
x dx
(d)
π/
2
0
cos
3
x dx
3. Perform the integration
x
√
x

1
dx
both by substitution and by integration by parts.
Reconcile the two answers.
4. The hypotenuse of a right triangle has length 13 meters and one side has length 5 meters.
Find the tangent of the angle adjacent to that side and the tangent of the angle opposite that
side.
5. A surveyor measures the angle of elevation of the top of a building as seen from a spot on the
ground at a distance of 100 feet from the building and finds it to be 1
.
25 radians. Given that
sin 1
.
25
≈
.
95 and cos 1
.
25
≈
.
39, estimate the height of the building.
6. The minute hand on the clock of the Vergessen Memorial Tower is 7 feet long. What is the
vertical speed in feet per minute of the tip of the minute hand at 12:15p.m.?
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 Spring '06
 Sarason
 Math, Trigonometry, Derivative, Integrals, triangle

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