GWC Math-G180
Homework/Study Guide
Chapter 6: Applications of the Integral
Spring 2015
1. (Sec 6.1)
Find the area of the region bounded by the graphs of y = x 2 2 x + 8 and =
y 12 x 2 .
Ans: 9
2. (Sec 6.1)
Find the area of the shaded region bounded by the
GWC Math-G180
Chapter 5: The Integral
Homework/Study Guide
Spring 2015
1. (Sec 5.1)
1
. Calculate R4 , L4 , and M 4 for the interval [1, 2] . Give your answer to
x2
four decimal places.
Ans: R4 0.4152,
=
=
L4 0.6027,
=
M 4 0.4955
Let f ( x) =
2. (Sec 5.1)
GWC Math-G180
Chapter 2: Limits
Homework/Study Guide
Spring 2015
1. (Sec 2.1)
The potential energy V of a pendulum of length 1 and mass 2, relative to its rest position
is=
V 2 g (1 cos ) .
Compute the average rate of change of the potential energy over t
GWC Math-G180
Homework/Study Guide
Chapter 3: Differentiation
Spring 2015
1. (Sec 3.1)
The derivative of the function x3 14 x + 7 at the point where x = 5 equals
Ans: 61
2. (Sec 3.1)
What is the derivative of the function x 4 2 x + 7 at the point where x
GWC Math-G180
Homework/Study Guide
Chapter 1: Precalculus Review
Spring 2015
1. (Sec 1.1)
Find the smallest and the largest values of x that satisfy each of the following
inequalities:
A) 3 x 7 8
B) 2 x 5 13
Ans:
1
A) xmin =
5
, xmax =
3
B) xmin =
4, xm
GWC Math-G180
Homework/Study Guide
Chapter 4: Applications of the Derivative
Spring 2015
1. (Sec 4.1)
Estimate the roots of the equation x 2 + 5 x + 2 =
0 using the linear approximation for
f ( x) = x .
Ans: 4.5625, 0.4375
2. (Sec 4.1)
Find the linearizat