Math 106: Review for Final Exam, Part II - SOLUTIONS
3
1. Use a second-order Taylor polynomial to estimate 28.
We choose f (x) = 3 x and x0 = 27 because 27 is the perfect cube closest to 28.
f (x) = x1/3
1
1
f (x) = x2/3 = 2/3
3
3x
2
2
f (x) = x5/3 = 5/3

Math 106 Fall 2014
Exam 3.2
December 10, 2014
1. Determine if the series is convergent or divergent by making a comparison (DCT or LCT) with a
suitable bn . Fill in the blanks with your answer. For Convergent or Divergent write Convergent or
C if the seri

Math 106 Fall 2014
Exam 3.1
December 10, 2014
1. Determine if the series is convergent or divergent by making a comparison (DCT or LCT) with a
suitable bn . Fill in the blanks with your answer. For Convergent or Divergent write Convergent or
C if the seri

Math 106: Review for Final Exam, Part I - SOLUTIONS
1. Find the following.
[See Review for Exam II for integration tips and strategies.]
(a) Let u = x3 , so du = 3x2 dx and du/3 = x2 dx.
12x2 cos(x3 ) dx =12
cos(x3 )x2 dx
.
du
3
= 4 sin(u) + C
= 12
cos(u)

Math 106: Review for Final Exam, Part II - SOLUTIONS
3
1. Use a second-order Taylor polynomial to estimate 28
28.
3
We choose f(x) = x and x0 = 27 because 27 is the perfect cube closest to 28.
f(x) = x1/3
1
1
f (x) = x2/3 = 2/3
3
3x
2
2
f (x) = x5/3 = 5/3

Math 106: Review for Final Exam, Part I - SOLUTIONS
1. Find the following.
[See Review for Exam II for integration tips and strategies.]
(a) Let u = x3 , so du = 3x2 dx and du/3 = x2 dx.
12x2 cos(x3 ) dx =12
cos(x3 )x2 dx
.
du
3
= 4 sin(u) + C
= 12
cos(u)