Review for Chapter 8 Individual Test
Name: _______________________________
Complete on Separate Paper:
Lesson 8.1.1 Limits at Infinity
1.
Identify the dominant term in each of the following expressions.
2.
a.
5x 3  4x 6  2x 2  1
b.
45x 3  27x 5  2x 8
c.
x 6  5x 2
d.
12x  4x 2  x 5  3
e.
53  3x 7  4x 2  5x
f.
17x  3 x 3
lim 3500(4 x )  5 x
c.
lim 5  4x  x 2
f.
Evaluate the following limits.
a.
d.
lim 12x 3  1.2 x
b.
lim  3x 2  42 log x
e.
x
x
x
x
Lesson 8.1.2 Limits of Rational Functions (at infinity)
1.
Evaluate the given limits.
a.
lim
(x 2 1)(x 2 1)
x (2x 2 3)(2x 2 5)
b.
3x 2  x2
x 5 x 2  4 x1
c.
lim
3x 3 x 2
x (x1)3
d.
7x 3  x
x (2x1)(3x 2 1)
e.
x2  4
x x 3  x1
f.
4 x 2  3x1
x 2 3x 2
lim
lim
lim
lim
Lesson 8.1.3 Limits of Rational Functions (at a point)
1.
Evaluate the given limits.
a.
lim
x 2 25
x5 x5
b.
x 2 9
x3 1  1
3 x
c.
lim
x1
x1 x 2 1
d.
x 2 9
2
x3 2 x  7 x 3
e.
11
4 x
x4 x 4
f.
x 3 8
x2 x 2  4
lim
lim
lim
lim
lim 15 x  x
x
lim x  4 x 5
x
Lesson 8.2.1 The Number e
1.
Evaluate each expression without using a calculator.
2.
a.
ln e 4
ln  1e 
b.
eln
c.
ln 5 x  ln 5 x1
d.
2 ln er
eln 1/ 
Evaluate the given limits.

x
lim 1  2x
a.

x
b.
7

x
lim 1  21x

x
Lesson 8.2.2 Applications of e
1.
Suppose $500,000 was invested with a 4% interest rate for a period of 20 years. What difference would there
be in the final value of the investment if the interest was invested continuously instead of monthly?
2.
$3,000 was invested for 8 years with the interest compounded continuously. If the investment is worth $7,700
at the end of 8 years, what was the interest rate?
3.
How long will it take any investment to quadruple if it earns 5.6% interest, compounded continuously?
4.
A 32 gram sample of radioactive iodine decays in such a way that the mass m (grams) remaining after t days is
given by:
m(t)  32e0.089t
a.
After how many days are there only 14 grams remaining?
b.
What is the half-life of the iodine?
Lesson 8.2.3 Infinite Geometric Series
1.
Find the given sum, or explain why it does not exist.
a.
1  23  94  278  ...
c.
3
5
e.
7  4 73  7  4 7  ...
 52  154  458  ...

2
3
 32  2 32  ...
b.
1
3
d.
47  45  43  4  ...
f.
2.5 1.75 1.225  0.8575  ...
Review Topics
1. Find an equation of a line that goes through the point (2, 5) and is parallel to y  2 x  4 . Write it in point-slope
form.
2. Find the point-slope form of the perpendicular bisector of segment AB where A   1, 4 and B   3,  2 .
3. Write the following in y 
a.
y
x5
x2
a
 k form:
xh
b.
y
3x  1
x 1
Answers to Chapter 8 Review Sheet
Lesson 8.1.1 Answers
1.
2.
a.
4x 6
b.
2x 8
c.
x6
d.
x5
e.
3x 7
f.
3 x3
a.

b.

c.

d.

e.

f.

Lesson 8.1.2 Answers
1.
2.
3.
a.
1
4
b.
3
5
c.
3
d.
7
6
e.
0
f.
4
3
a.
2, –1, 12 , 2, –1
b.
–1, –9, –33, –105, –321
c.
2, 1, 4, –9, –116
d.
1, 3, 12, 96, 2496
b.
8, 4, 2, 1, 12
3, –2, –7, –12, –17
bn  5n  8
bn  8
Lesson 8.1.3 Answers
1.
a.
10
b.
54
c.
1
2
d.
6
5
e.
1
 16
f.
3
Lesson 8.2.1 Answers
1.
a.
–4
b.
7
c.
ln 5
d.
2 r
12 
n1
Lesson 8.2.2 Answers
1.
$1480.42
2.
11.78%
3.
24.76 years
4.
a.
9.3 days
b.
7.79 days
Lesson 8.2.3 Answers
1.
2.
a.
3
5
b.
1
3 2
c.
9
5
d.
164 7
17
e.
 18.17
f.
25
3
a.
49
198
b.
5 11
90
c.
5
7 99
d.
98
2 225
 15420.24
 8 13