November 25, 2009
MATH 27 X
RECITATION CLASS
28
ANSWER KEY FOR ACTIVITY 3
Derivatives of Logarithmic Functions;
Integrals Yielding Inverse Trigonometric Functions and Logarithmic Functions
Show a detailed solution for each problem. Write the word Solution

SIGNATURE OVER PRINTED NAME: _
RECITATION INSTRUCTOR: _
STUDENT NO.:_
RECITATION SECTION: _
January 27, 2010
MATH 27 X
RECITATION CLASS
ANSWER KEY FOR ACTIVITY 9
Px
Evaluating Integrals of the form
dx
Qx
33
by the Method of Partial Fraction Decompositio

Applications of the Derivative
1. A woman sitting on top of a vertical cliff 200 feet above sea level watches a motorboat that
is moving directly away from the foot of the cliff. The angle of depression of the motorboat
is decreasing at a rate of 0.08 rad

Evaluating Limits that are Indeterminate in Form
1.
lim
x 0
tan x x
x sin x
Solution:
tan x x 0
sec2 x 1 0
lim
lim
x 0 x sin x 0
x0 1 cos x 0
1
1
2
1 cos 2 x
1 cos x
cos
x
lim
lim
lim
2
x 0 1 cos x
x 0 1 cos x cos 2 x
x 0 cos 2 x
2.
1
1
lim
x

SIGNATURE OVER PRINTED NAME: _
STUDENT NO.:_
RECITATION INSTRUCTOR: _
RECITATION SECTION: _
January 20, 2010
MATH 27 X
RECITATION CLASS
ACTIVITY 8
42
Evaluating Integrals containing Powers Of Trigonometric Functions or
Forms
2
a u , u a or u a
2
2
2
2
2
G

SIGNATURE OVER PRINTED NAME: _ RECITATION SECTION: _
STUDENT NO.:_
RECITATION INSTRUCTOR: _
January 13, 2010
MATH 27 X
RECITATION CLASS
30
ACTIVITY 7
1.
Evaluating Integrals by the Method of Integration-By-Parts
sin 2 x cos x dx
Solution:
Let u sin 2 x du