Precalculus with Limits: A Graphing Approach 5e, Warm-Up Exercises and Daily Homework Quiz TransparenciesCopyright © Houghton Mifflin Company. All rights reserved.

99

SECTION 11.1

WARM-UP EXERCISES

Evaluate the function at the x-values 1.9, 1.99, and 1.999.

1. f (x ) = 3x −1 2. f (x ) =

x − 2

x 2 + x − 63.

f (x ) =

sin(x − 2)

3x − 6

4. In which quadrant(s) is the graph of xy < 0?

Sketch the graph of the function.

5. f (x ) =

x −1, x < 3

1− x, x ≥ 3

⎧⎨⎩

6. f (x ) =

2, x ≤ 0

−1, x > 0

⎧⎨⎩

DAILY HOMEWORK QUIZ

Suppose that limx→c

f (x ) = −4 and limx→c

g(x ) = 1. Evaluate the limit.

1. limx→c

3f (x )

2g(x ) 2.

limx→c

2− 4g(x )⎡⎣

⎤⎦ 3.

limx→c

f (x )g(x )

Find the limit by direct substitution.

4. lim

x→−1x + 5 5.

limx→7

(x 2 − 3x − 20) 6. lim

x→−πsec x

ANSWERS

WU 1. 4.7; 4.97; 4.997 2. 0.2041; 0.2004; 0.2000

3. 0.3328; 0.3333; 0.3333 4. Quadrants II and IV

5. 6.

QUIZ 1. –6 2. 0 3. –4 4. 25. 8 6. –1

Precalculus with Limits: A Graphing Approach 5e, Warm-Up Exercises and Daily Homework Quizzes TransparenciesCopyright © Houghton Mifflin Company. All rights reserved.

100

SECTION 11.2

WARM-UP EXERCISES

Create a table of values for the function and use the result to estimate the limitnumerically. Use a graphing utility to graph the corresponding function to confirm yourresult graphically.

1. lim

x→−1

x +1

x 2 −12.

limx→0

x + 3 − 3

x

3. limx→1

1

x−1

x −14.

limx→0

sinx

2x

Suppose that limx→c

f (x ) = 2 and limx→c

g(x ) = 3. Evaluate the limit.

5. limx→c

f (x )

g(x )6.

limx→c

[3f (x )− 2g(x )]2

DAILY HOMEWORK QUIZ

Find the limit (if it exists). Use a graphing utility to verify your result graphically.

1. limx→3

x − 3

x 2 − 9

2. limx→0

2x +1−1

x

3. lim

x→−1

x +1

x 3 +1

Find limh→0

f (x + h)− f (x )

h.

4. f (x ) =

2

x +1

5. f (x ) = 3x 2 + 2

Precalculus with Limits: A Graphing Approach 5e, Warm-Up Exercises and Daily Homework Quiz TransparenciesCopyright © Houghton Mifflin Company. All rights reserved.

101

ANSWERS

WU 1.

2.

3.

4.

5.

2

36. 0

QUIZ 1.

1

62. 1 3.

1

3

4.

−2

(x +1)25. 6x

x –1.1 –1.01 –1.001 –1 –0.999 –0.99 –0.9f(x) –0.4762 –0.4975 –0.4998 –0.5 –0.5003 –0.5025 –0.5263

x 0.9 0.99 0.999 1 1.001 1.01 1.1f(x) –1.111 –1.0101 –1.001 –1 –0.9990 –0.9901 –0.9091

x –0.1 –0.01 –0.001 0 0.001 0.01 0.1f(x) 0.4992 0.5000 0.5000 0.5 0.5000 0.5000 0.4992

x –0.1 –0.01 –0.001 0 0.001 0.01 0.1f(x) 0.2911 0.2899 0.2887 0.2887 0.2887 0.2884 0.2863

Precalculus with Limits: A Graphing Approach 5e, Warm-Up Exercises and Daily Homework Quizzes TransparenciesCopyright © Houghton Mifflin Company. All rights reserved.

102

SECTION 11.3

WARM-UP EXERCISES

Find limh→0

f (x + h)− f (x )

h.

1. f (x ) = 2x −1

2. f (x ) = x −1

3. f (x ) =

1

x − 3

4. f (x ) = x 2 + 2x

DAILY HOMEWORK QUIZ

Use the limit process to find the slope of the graph of the function at the specifiedpoint. Use a graphing utility to confirm your result.

1. f (x ) = 1− x , (−8, 3) 2. f (x ) =

2

x, (2, 1) 3. f (x ) = 2x − x 2 , (−1, −3)

Find the derivative of the function.

4. f (x ) =

2

x5.

f (x ) = −

1

x + 36. f (x ) = 3x 2 + 6x

ANSWERS

WU 1. 2 2.

1

2 x −13.

−1

(x − 3)24. 2x + 2

QUIZ 1. −

1

62.

−

1

23. 4 4.

−

1

x 3

5.

1

(x + 3)26. 6x + 6

Precalculus with Limits: A Graphing Approach 5e, Warm-Up Exercises and Daily Homework Quiz TransparenciesCopyright © Houghton Mifflin Company. All rights reserved.

103

SECTION 11.4

WARM-UP EXERCISES

Find the derivative of the function.

1. f (x ) = 2x 2 − 4 2. f (x ) = −

1

x 23. f (x ) = 13

Find the first 5 terms of the sequence. Assume n begins with 1.

4. a

n=

n −1

n5.

a

n=

(n +1)!

(n + 2)!6. an

= (−1)n+1n2

DAILY HOMEWORK QUIZ

Find the limit (if it exists). If the limit does not exist, explain why. Use a graphing utilityto verify your result graphically.

1. limx→∞

12

x 32.

limx→∞

(2x −1)2

3x 23.

lim

x→−∞4 −

2x 2 +1

x 2

Find the limit of the sequence. Then verify the limit numerically by using a graphingutility.

4. a

n=

1

nn −

1

n

n(n −1)

2

⎡

⎣⎢

⎤

⎦⎥

⎛

⎝⎜⎞

⎠⎟

5. a

n=

9

n3

2n(2n +1)(2n + 2)

24

⎡

⎣⎢

⎤

⎦⎥

ANSWERS

WU 1. 4x 2.

2

x 33. 0

4. 0,

1

2,2

3,3

4,4

55.

1

3,1

4,1

5,1

6,1

76. 1, –4, 9, –16, 25

QUIZ 1. 0 2.

4

33. 2 4.

1

25. 3

Precalculus with Limits: A Graphing Approach 5e, Warm-Up Exercises and Daily Homework Quizzes TransparenciesCopyright © Houghton Mifflin Company. All rights reserved.

104

SECTION 11.5

WARM-UP EXERCISES

Evaluate the sum.

1.

2nn=1

6

∑ 2.

n

n +1n=1

4

∑ 3.

(−1)n n!n=0

4

∑Find the sum of the infinite geometric series.

4.

3

4

⎛⎝⎜

⎞⎠⎟

n

n=1

∞

∑ 5.

3 0.2( )n

n=0

∞

∑

DAILY HOMEWORK QUIZ

Evaluate the sum using the summation formulas and properties.

1.

2i=1

40

∑ 2.

i 2

i=1

23

∑ 3.

(2 j 2 − j 3

i=1

11

∑ )

Use the limit process to find the area of the region between the graph of the functionand the x-axis over the interval [0, 2].

4. g(x ) = 2x +1

5. f (x ) = 4 − x 2

6. f (x ) =

1

2(x 3 + x )

ANSWERS

WU 1. 42 2.

163

603. 19

4. 4 5. 3.75

QUIZ 1. 80 2. 4324 3. –3344

4. 6 5.

16

36. 3