CHAPTER 1
Limits and Their Properties
Section 1.1

A Preview of Calculus . . . . . . . . . . . . . . . . . . . 305

Section 1.2

Finding Limits Graphically and Numerically . . . . . . . 305

Section 1.3

Evaluating Limits Analytically . . . . . . . . . . . . . . . 309

Section 1.4

Continuity and One-Sided Limits

Section 1.5

Infinite Limits

Review Exercises

. . . . . . . . . . . . . 315

. . . . . . . . . . . . . . . . . . . . . . . 320

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

CHAPTER 1
Limits and Their Properties
Section 1.1

A Preview of Calculus

Solutions to Even-Numbered Exercises
2. …ver más…

f x

x→3

4 0 be given. Take

0. Let

m

.

Evaluating Limits Analytically

xc

such that 0 < x
If 0 < x

c<

b

mc

b

x→c

2.

mc

L < 1L
2

b.

(a) lim g x

2.4

(b) lim g x

,x

c,

> 0.

4

x→4

x→0

0

4.

(a) lim f t

10

t→4

0

(b) lim f t
−5

5

t→ 1

10

10

−5

− 10

12

x x 2

x→ 2

x2

10. lim

x→1

14. lim

x→ 3

18. lim

x→3

3

3

x x 22. lim 2x x→0 1

1

4

2

3

2x2

4

x→ 3

2

1

2
3

1
4

31
34
3

12. lim 3x3

0

x→1

2

20

3
5

4

16. lim

x→3

2

1

2x x 20. lim 3 x

2

2

1

tt

8. lim 3x

8

2 x ft

9

6. lim x3

x→4

3

1

23
3

3

42

(c) lim g f x

x→4

(b) lim g x

2 42

34

3

6

21

x → 21

(c) lim g f x

g 21

x→4

30. lim sin x→1 x
2

lim cos x

x→5

3

sin

cos

5
3

21

28. lim tan x

tan

x→

3

21

3
8

4

2

7

4

16
16

0

3
3

32. lim cos 3x

1

2

1

7

3
5

g4

x→ 3

2

31

3

x→ 3 x→4 26. (a) lim f x

3

4

24. (a) lim f x
(b) lim g x

34.

,c

Evaluating Limits Analytically

10

gx

1
2 L.

L<

implies g x

Hence for x in the interval c

<

b

which shows that lim mx

Section 1.3

1