Calculus for scientists and engineers early transcendentals 1st edition briggs test bank

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the average velocity of the function over the given interval.
1) y = x2 + 3x, [1, 8]
88
A)
7

21
B)
2

1)

C) 11

D) 12

2) y = 9x3 + 5x2 - 8, [-2, 8]
A) 492

3) y =

C) 615

D) 498

C) 7

3
D) 10

2x, [2, 8]

3)
1
B)
3

A) 2

4) y =

2)
1245
B)
2

3
, [4, 7]
x-2

A) -

3
10

5) y = 4x2 , 0,
A)

4)
B) 7

C) -

B) 2

7) h(t) = sin (3t), 0,

8) g(t) = 4 + tan t, -

3
10

D) 7

6)
B) -2

C) -

1
6

D) -34

π
6

6
π

3
2

D) 2

5)

6) y = -3x2 - x, [5, 6]
1
A)
2

A) -

1
3

7
4

1
3

A) -

C)

7)
B)

π
6

C)

3
π

D)

6
π

π π
,
4 4

8)
B) -

4
π

C)

1

4
π

D) 0


Use the table to find the instantaneous velocity of y at the specified value of x.
9) x = 1.
x y
0 0
0.2 0.02
0.4 0.08
0.6 0.18
0.8 0.32
1.0 0.5
1.2 0.72
1.4 0.98
A) 0.5

B) 2

C) 1

9)

D) 1.5

10) x = 1.
x y
0 0
0.2 0.01
0.4 0.04
0.6 0.09

0.8 0.16
1.0 0.25
1.2 0.36
1.4 0.49
A) 1.5

10)

B) 2

C) 1

D) 0.5

11) x = 1.
x y
0 0
0.2 0.12
0.4 0.48
0.6 1.08
0.8 1.92
1.0 3
1.2 4.32
1.4 5.88
A) 8

11)

B) 6

C) 2

2

D) 4


12) x = 2.
x y
0 10
0.5 38
1.0 58
1.5 70
2.0 74
2.5 70
3.0 58
3.5 38
4.0 10
A) 0

12)

B) 4

C) 8

D) -8

13) x = 1.
x

y
0.900 -0.05263
0.990 -0.00503
0.999 -0.0005
1.000 0.0000
1.001 0.0005
1.010 0.00498
1.100 0.04762
A) 0.5

13)

B) -0.5

C) 0

D) 1

Find the slope of the curve for the given value of x.
14) y = x2 + 5x, x = 4
1
A) slope is
20
15) y = x2 + 11x - 15, x = 1
1
A) slope is
20
16) y = x3 - 5x, x = 1
A) slope is -3

14)

B) slope is -39

4
C) slope is 25

B) slope is -39

4
C) slope is 25

D) slope is 13

15)
D) slope is 13

16)
C) slope is -2

B) slope is 1

D) slope is 3

17) y = x3 - 2x2 + 4, x = 3
A) slope is 1

B) slope is -15

C) slope is 15

D) slope is 0

18) y = 2 - x3 , x = -1
A) slope is 0

B) slope is 3

C) slope is -3

D) slope is -1

17)

18)

3


Solve the problem.
19) Given lim f(x) = Ll, lim f(x) = Lr, and Ll ≠ Lr, which of the following statements is true?
x→0 x→0 +
I.

lim f(x) = Ll
x→0

II.

lim f(x) = Lr

x→0

19)

III. lim f(x) does not exist.
x→0
A) none
20) Given

B) I

C) III

D) II

lim f(x) = Ll, lim f(x) = Lr , and Ll = Lr, which of the following statements is false?
x→0 x→0 +

I.

lim f(x) = Ll
x→0

II.

lim f(x) = Lr
x→0

20)

III. lim f(x) does not exist.
x→0
A) I

B) III

C) II

D) none

21) If lim f(x) = L, which of the following expressions are true?
x→0
I.

lim f(x) does not exist.
x→0 -

II.

lim f(x) does not exist.
x→0 +

III.

lim f(x) = L
x→0 -

IV.

lim f(x) = L

x→0 +

A) I and II only

B) I and IV only

C) III and IV only

21)

D) II and III only

22) What conditions, when present, are sufficient to conclude that a function f(x) has a limit as x
approaches some value of a?
A) Either the limit of f(x) as x→a from the left exists or the limit of f(x) as x→a from the right
exists
B) f(a) exists, the limit of f(x) as x→a from the left exists, and the limit of f(x) as x→a from the
right exists.
C) The limit of f(x) as x→a from the left exists, the limit of f(x) as x→a from the right exists, and
at least one of these limits is the same as f(a).
D) The limit of f(x) as x→a from the left exists, the limit of f(x) as x→a from the right exists, and
these two limits are the same.

4

22)


Use the graph to evaluate the limit.
23) lim f(x)

x→-1

23)

y

1

-6 -5 -4 -3 -2 -1

1

2

3

4

5

6 x

-1

A)

3
4

B) ∞

C) -1

D) -

3
4

24) lim f(x)
x→0

24)
y
4
3
2
1

-4

-3

-2

-1

1

2

3

4 x

-1
-2
-3
-4

A) -2

B) 2

C) 0

5

D) does not exist


25) lim f(x)
x→0

25)
6

y

5
4

3
2
1
-6 -5 -4 -3 -2 -1
-1

1

2

3

4

5

6 x

-2
-3
-4
-5
-6

A) 0

C) -1

B) does not exist

D) 1

26) lim f(x)
x→0

26)

12

y

10
8
6
4
2
-2

-1

1

2

3

4

5

x

-2
-4

A) -1

B) 6

C) 0

6

D) does not exist


27) lim f(x)
x→0

27)

y
4
3
2
1
-4

-3

-2

-1

1

2

3

4 x

-1
-2
-3
-4

A) -1

B) does not exist

C) 1

D) ∞

28) lim f(x)
x→0

28)

y
4
3
2
1
-4

-3

-2

-1

1

2

3

4 x

-1
-2
-3
-4

A) ∞

C) -1

B) does not exist

7

D) 1


29) lim f(x)
x→0

29)
y
4
3
2
1

-4

-3

-2

-1

1

2

3

4

x

-1
-2
-3
-4

A) 2

B) does not exist

C) 0

D) -2

30) lim f(x)
x→0

30)
y
4
3
2
1

-4

-3

-2

-1

1

2

3

4

x

-1
-2
-3
-4

A) does not exist

C) -2

B) 0

8

D) 1

31) lim f(x)
x→0

31)
y
4
3
2
1

-4

-3

-2

-1

1

2

3

x

4

-1
-2
-3
-4

B) -1

A) 2
32) Find

C) does not exist

D) -2

lim f(x) and
lim
f(x)
x→(-1)x→(-1)+

32)

y
2

-4

-2

2

4

x

-2

-4

-6

A) -7; -5

B) -7; -2

C) -5; -2

9

D) -2; -7


Use the table of values of f to estimate the limit.
33) Let f(x) = x2 + 8x - 2, find lim f(x).
x→2
x
f(x)

1.9

1.99

1.999

33)

2.001

2.01

2.1

A)
x 1.9
1.99 1.999 2.001 2.01 2.1
; limit = ∞
f(x) 5.043 5.364 5.396 5.404 5.436 5.763
B)
x 1.9
1.99 1.999 2.001 2.01 2.1
; limit = 5.40
f(x) 5.043 5.364 5.396 5.404 5.436 5.763
C)
x
1.9
1.99
1.999 2.001 2.01
2.1
; limit = 18.0
f(x) 16.810 17.880 17.988 18.012 18.120 19.210
D)

x
1.9
1.99
1.999 2.001 2.01
2.1
; limit = 17.70
f(x) 16.692 17.592 17.689 17.710 17.808 18.789
34) Let f(x) =

x
f(x)

x-4
, find lim f(x).
x-2
x→4
3.9

3.99

3.999

34)

4.001

4.01

4.1

A)
x 3.9
3.99
3.999
4.001
4.01
4.1
; limit = 5.10
f(x) 5.07736 5.09775 5.09978 5.10022 5.10225 5.12236
B)
x 3.9
3.99
3.999
4.001
4.01
4.1
; limit = 4.0
f(x) 3.97484 3.99750 3.99975 4.00025 4.00250 4.02485
C)
x 3.9
3.99
3.999
4.001
4.01
4.1
; limit = 1.20
f(x) 1.19245 1.19925 1.19993 1.20007 1.20075 1.20745
D)
x 3.9
3.99

3.999
4.001
4.01
4.1
; limit = ∞
f(x) 1.19245 1.19925 1.19993 1.20007 1.20075 1.20745

10


35) Let f(x) = x2 - 5, find lim f(x).
x→0
-0.1

x
f(x)

-0.01

35)

-0.001

0.001

0.01

0.1

A)

x -0.1
f(x) -4.9900

-0.01
-4.9999

-0.001
-5.0000

0.001
0.01
0.1
; limit = -5.0
-5.0000 -4.9999 -4.9900

x -0.1
f(x) -2.9910

-0.01
-2.9999

-0.001
-3.0000

0.001
0.01
0.1
; limit = -3.0
-3.0000 -2.9999 -2.9910

x -0.1
f(x) -1.4970

-0.01
-1.4999

-0.001
-1.5000

0.001
0.01
0.1
; limit = -15.0
-1.5000 -1.4999 -1.4970

x -0.1
f(x) -1.4970

-0.01
-1.4999

-0.001
-1.5000

0.001
0.01
0.1
; limit = ∞
-1.5000 -1.4999 -1.4970

B)

C)

D)

36) Let f(x) =

x
f(x)

x+2
x2 + 5x + 6
-2.1

, find

lim f(x).
x→-2

-2.01

-2.001

36)

-1.999

-1.99

-1.9

A)
x -2.1
-2.01 -2.001 -1.999 -1.99
-1.9 ; limit = 0.9
f(x) 1.0111 0.9101 0.9010 0.8990 0.8901 0.8091
B)
x
-2.1
-2.01
-2.001 -1.999
-1.99
-1.9 ; limit = -1
f(x) -1.1111 -1.0101 -1.0010 -0.9990 -0.9901 -0.9091
C)
x -2.1
-2.01 -2.001 -1.999 -1.99
-1.9 ; limit = 1
f(x) 1.1111 1.0101 1.0010 0.9990 0.9901 0.9091
D)
x -2.1
-2.01 -2.001 -1.999 -1.99
-1.9 ; limit = 1.1
f(x) 1.2111 1.1101 1.1010 1.0990 1.0901 1.0091

11


37) Let f(x) =

x2 + 3x + 2
, find lim f(x).
x2 - 2x - 3
x→-1
-1.1

x
f(x)

-1.01

37)

-1.001

-0.999

-0.99

-0.9

A)
x
-1.1
-1.01
-1.001 -0.999
-0.99
-0.9 ; limit = -1.5
f(x) -1.3810 -1.4876 -1.4988 -1.5013 -1.5126 -1.6316

B)
x
-1.1
-1.01
-1.001 -0.999
-0.99
-0.9 ; limit = -0.15
f(x) -0.1195 -0.1469 -0.1497 -0.1503 -0.1531 -0.1821
C)
x
-1.1
-1.01
-1.001 -0.999
-0.99
-0.9 ; limit = -0.25
f(x) -0.2195 -0.2469 -0.2497 -0.2503 -0.2531 -0.2821
D)
x
-1.1
-1.01
-1.001 -0.999
-0.99
-0.9 ; limit = -0.35
f(x) -0.3195 -0.3469 -0.3497 -0.3503 -0.3531 -0.3821
38) Let f(x) =

x
f(x)

sin(8x)

, find lim f(x).
x
x→0

-0.1

-0.01
7.9914694

-0.001

38)

0.001

0.01
7.9914694

A) limit = 7.5
C) limit = 0
39) Let f(θ) =

0.1

B) limit does not exist
D) limit = 8

cos (6θ)
, find lim f(θ).
θ

θ→0

x
-0.1
f(θ) -8.2533561

-0.01

-0.001

39)

0.001

A) limit = 0
C) limit = 8.2533561

0.01

0.1
8.2533561

B) limit does not exist
D) limit = 6

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
40) It can be shown that the inequalities 1 -

x2

x sin(x)
<
< 1 hold for all values of x close
6
2 - 2 cos(x)

to zero. What, if anything, does this tell you about

x sin(x)
? Explain.
2 - 2 cos(x)

12

40)


MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
41) Write the formal notation for the principle "the limit of a quotient is the quotient of the limits" and
include a statement of any restrictions on the principle.
g(x) g(a)
A) lim
, provided that f(a) ≠ 0.
=
f(a)
x→a f(x)
g(x)
B) If lim g(x) = M and lim f(x) = L, then lim
=
x→a

x→a
x→a f(x)

lim g(x)
x→a
lim f(x)
x→a

=

41)

M
, provided that
L

f(a) ≠ 0.
lim g(x)
x→a
g(x)
M
C) If lim g(x) = M and lim f(x) = L, then lim
=
= , provided that
f(x)
lim
f(x)
L
x→a
x→a

x→a
x→a
L ≠ 0.
g(x) g(a)
D) lim
.
=
f(a)
x→a f(x)
42) Provide a short sentence that summarizes the general limit principle given by the formal notation
lim [f(x) ± g(x)] = lim f(x) ± lim g(x) = L ± M, given that lim f(x) = L and lim g(x) = M.
x→a
x→a
x→a
x→a
x→a

42)

A) The limit of a sum or a difference is the sum or the difference of the limits.
B) The limit of a sum or a difference is the sum or the difference of the functions.
C) The sum or the difference of two functions is the sum of two limits.
D) The sum or the difference of two functions is continuous.
43) The statement "the limit of a constant times a function is the constant times the limit" follows from
a combination of two fundamental limit principles. What are they?
A) The limit of a product is the product of the limits, and the limit of a quotient is the quotient of
the limits.
B) The limit of a function is a constant times a limit, and the limit of a constant is the constant.
C) The limit of a product is the product of the limits, and a constant is continuous.
D) The limit of a constant is the constant, and the limit of a product is the product of the limits.

Find the limit.
44) lim
x→15
A)
45)

3
15

46)

44)
B) 15

C)

3

D) 3

lim (5x - 4)
x→-9
A) -41

45)
B) -49

C) 49

D) 41

lim (6 - 5x)
x→-15
A) 81

43)

46)
B) -81

C) 69

13

D) -69


Give an appropriate answer.
47) Let lim f(x) = -9 and lim g(x) = -3. Find lim [f(x) - g(x)].
x → -8
x → -8
x → -8
A) -8
48) Let

C) -12

D) -6

lim f(x) = -10 and lim g(x) = 6. Find lim [f(x) ∙ g(x)].

x → -7
x → -7
x → -7

A) -4

49) Let

B) -9

47)

B) -7

48)
D) -60

C) 6

f(x)
lim f(x) = -4 and lim g(x) = -2. Find lim
.
g(x)
x → -9
x → -9
x → -9

A)

1

2

B) -9

50) Let lim f(x) = 169. Find lim
x→5
x→5
A) 169

C) -2

49)
D) 2

f(x).

50)

B) 3.6056

C) 13

D) 5

51) Let lim f(x) = -3 and lim g(x) = 1. Find lim [f(x) + g(x)]2 .
x→5
x→5
x→5
A) -4

52) Let

lim f(x) = 1024. Find lim
x → 10
x → 10

A) 10

53) Let

B) -2

C) 4
5

5
6

52)

B) 4

B)

D) 10

f(x).
C) 5

lim f(x) = -1 and lim g(x) = -1. Find lim

x→ -6
x→ -6
x→ -6

A) -

51)

5
2

D) 1024

-5f(x) - 10g(x)
.
7 + g(x)
C) -6

53)
D) -

65
7

Find the limit.
54) lim (x3 + 5x2 - 7x + 1)
x→2
A) 15

54)

B) does not exist

C) 29

D) 0

55) lim (2x5 - 3x4 + 4x3 + x2 + 5)
x→2
A) 153

56)

55)
C) -7

B) 25

D) 57

x
lim
3x
+2
x→-1
A) 0

56)
C) -

B) does not exist

14

1
5

D) 1


57) lim
x→0

x3 - 6x + 8
x-2

A) 4

57)
B) Does not exist

D) -4

C) 0

3x2 + 7x - 2
58) lim
x→1 3x2 - 4x - 2
A) -

7

4

58)
C) -

B) 0

8
3

D) Does not exist

59) lim (x + 2)2 (x - 3)3
x→1
A) -8
60) lim
x→7

D) 64

x2 + 12x + 36

60)
B) does not exist

C) 169

D) ±13

4x + 45

lim
x→-6
A)

C) -72

B) 576

A) 13
61)

59)

21

62) lim
h→0

A) 1/4

B) -21

C) 21

D) - 21

2
3h + 4 + 2

A) Does not exist

63) lim
x→0

61)

62)
B) 1/2

C) 2

D) 1

1+x-1
x

63)
B) 1/2

C) Does not exist

D) 0

Determine the limit by sketching an appropriate graph.
for x < 7
64) lim f(x), where f(x) = -2x + 4
4x
5
for x ≥ 7

+
x → 7A) 33
65)

66)

B) 6

lim f(x), where f(x) = -2x + 0
3x + 1
x → 3+
A) 2

C) 5

D) -10

for x < 3
for x ≥ 3

65)
C) -6

B) 10

2
lim f(x), where f(x) = x + 6
0
x → 3+
A) 3

64)

D) 1

for x ≠ 3
for x = 3

66)

B) 9

C) 15

15

D) 0


67)

lim f(x), where f(x) =
x → 6A) 0

68)

lim f(x), where f(x) =
x → -4 +
A) Does not exist

9 - x2
3
6
B) 3

0≤x<3
3≤x<6
x=6

67)
C) 6

2x
2
0
B) -0

D) Does not exist

-4 ≤ x < 0, or 0 < x ≤ 1
x=0
x < -4 or x > 1
C) 2

68)
D) -8

Find the limit, if it exists.
x3 + 12x2 - 5x
69) lim

5x
x→0
A) Does not exist

69)
B) -1

C) 0

D) 5

x4 - 1
70) lim
x→1 x - 1
A) Does not exist

71)

lim
x → -8

lim
x→6

lim
x→1

71)
C) Does not exist

D) 1

72)
B) 272

C) 1

D) 17

x2 + 3x - 54
x-6

73)
B) Does not exist

C) 0

D) 15

x2 + 8x - 9
x2 - 1

74)
B) - 4

A) 0

75)

D) 2

x2 + 17x + 72
x+8

A) 3

74)

C) 4

B) 4

A) Does not exist

73)

B) 0

x2 - 4
lim
x→2 x-2
A) 2

72)

70)

C) Does not exist

D) 5

x2 - 1
lim
x → 1 x2 - 6x + 5
A) -

1
2

75)
C) -

B) 0

1
4

D) Does not exist

x2 - 9x + 18
76) lim
x→3 x2 - 8x + 15
A) Does not exist

76)
B) -

3
2

C)

16

3
2

D) -

9
2


77)

lim
h→0

(x + h)3 - x3
h

A) 3x2 + 3xh + h2

78)

lim
x → 10

77)
B) 3x2

C) 0

D) Does not exist

10 - x
10 - x

78)

A) 0

B) Does not exist

D) -1

C) 1

Provide an appropriate response.
79) It can be shown that the inequalities -x ≤ x cos

1
≤ x hold for all values of x ≥ 0.
x

79)

1
Find lim x cos
if it exists.

x
x→0
A) 1

B) 0.0007

80) The inequality 1Find lim
x→0

C) 0

D) does not exist

x2 sin x
<
< 1 holds when x is measured in radians and x < 1.
2
x

sin x
if it exists.
x

A) does not exist

B) 1

C) 0.0007

D) 0

81) If x3 ≤ f(x) ≤ x for x in [-1,1], find lim f(x) if it exists.
x→0
A) does not exist

B) -1

81)
C) 1

D) 0

Compute the values of f(x) and use them to determine the indicated limit.
82) If f(x) = x2 + 8x - 2, find lim f(x).
x→2
x
f(x)

1.9

80)

1.99

1.999

2.001

2.01

82)

2.1

A)
x 1.9
1.99 1.999 2.001 2.01 2.1
; limit = ∞
f(x) 5.043 5.364 5.396 5.404 5.436 5.763
B)
x
1.9
1.99
1.999 2.001 2.01
2.1
; limit = 17.70
f(x) 16.692 17.592 17.689 17.710 17.808 18.789
C)
x 1.9
1.99 1.999 2.001 2.01 2.1
; limit = 5.40
f(x) 5.043 5.364 5.396 5.404 5.436 5.763
D)
x
1.9
1.99
1.999 2.001 2.01
2.1
; limit = 18.0
f(x) 16.810 17.880 17.988 18.012 18.120 19.210

17


83) If f(x) =

x
f(x)

x4 - 1
, find lim f(x).
x-1
x→1
0.9

0.99

83)

0.999

1.001

1.01

1.1

A)
x 0.9
0.99 0.999 1.001 1.01 1.1

; limit = ∞
f(x) 1.032 1.182 1.198 1.201 1.218 1.392
B)
x 0.9
0.99 0.999 1.001 1.01 1.1
; limit = 4.0
f(x) 3.439 3.940 3.994 4.006 4.060 4.641
C)
x 0.9
0.99 0.999 1.001 1.01 1.1
; limit = 5.10
f(x) 4.595 5.046 5.095 5.105 5.154 5.677
D)
x 0.9
0.99 0.999 1.001 1.01 1.1
; limit = 1.210
f(x) 1.032 1.182 1.198 1.201 1.218 1.392

84) If f(x) =

x
f(x)

x3 - 6x + 8
, find lim f(x).
x-2
x→0
-0.1

-0.01

-0.001

84)

0.001

0.01

0.1

A)
x -0.1
0.001
0.01
0.1
-0.01
-0.001
; limit = -2.10
f(x) -2.18529 -2.10895 -2.10090 -2.99910 -2.09096 -2.00574
B)
x -0.1
0.001
0.01
0.1
-0.01
-0.001
; limit = ∞
f(x) -1.22843 -1.20298 -1.20030 -1.19970 -1.19699 -1.16858
C)

x -0.1
0.001
0.01
0.1
-0.01
-0.001
; limit = -4.0
f(x) -4.09476 -4.00995 -4.00100 -3.99900 -3.98995 -3.89526
D)
x -0.1
0.001
0.01
0.1
-0.01
-0.001
; limit = -1.20
f(x) -1.22843 -1.20298 -1.20030 -1.19970 -1.19699 -1.16858

18


85) If f(x) =

x
f(x)

x-4
, find lim f(x).
x-2
x→4

3.9

3.99

85)

3.999

4.001

4.01

4.1

A)
x 3.9
3.99
3.999
4.001
4.01
4.1
; limit = 4.0
f(x) 3.97484 3.99750 3.99975 4.00025 4.00250 4.02485
B)
x 3.9
3.99
3.999
4.001
4.01
4.1

; limit = 1.20
f(x) 1.19245 1.19925 1.19993 1.20007 1.20075 1.20745
C)
x 3.9
3.99
3.999
4.001
4.01
4.1
; limit = ∞
f(x) 1.19245 1.19925 1.19993 1.20007 1.20075 1.20745
D)
x 3.9
3.99
3.999
4.001
4.01
4.1
; limit = 5.10
f(x) 5.07736 5.09775 5.09978 5.10022 5.10225 5.12236
86) If f(x) = x2 - 5, find

x
f(x)

-0.1

lim f(x).
x→0
-0.01

86)

-0.001

0.001

0.01

0.1

A)
x -0.1
f(x) -1.4970

-0.01
-1.4999

-0.001
-1.5000

0.001
0.01
0.1
; limit = ∞
-1.5000 -1.4999 -1.4970

x -0.1
f(x) -2.9910

-0.01
-2.9999

-0.001
-3.0000

0.001
0.01
0.1
; limit = -3.0
-3.0000 -2.9999 -2.9910

x -0.1
f(x) -1.4970

-0.01
-1.4999

-0.001
-1.5000

0.001
0.01
0.1
; limit = -15.0
-1.5000 -1.4999 -1.4970

x -0.1
f(x) -4.9900

-0.01
-4.9999

-0.001
-5.0000

0.001
0.01
0.1
; limit = -5.0
-5.0000 -4.9999 -4.9900

B)

C)

D)

19


87) If f(x) =

x
f(x)

x+1
, find lim f(x).
x+1
x→1

0.9

0.99

87)

0.999

1.001

1.01

1.1

A)
x 0.9
0.99
0.999
1.001
1.01
1.1
; limit = ∞
f(x) 0.21764 0.21266 0.21219 0.21208 0.21160 0.20702
B)
x 0.9
0.99
0.999
1.001
1.01
1.1

; limit = 0.7071
f(x) 0.72548 0.70888 0.70728 0.70693 0.70535 0.69007
C)
x 0.9
0.99
0.999
1.001
1.01
1.1
; limit = 0.21213
f(x) 0.21764 0.21266 0.21219 0.21208 0.21160 0.20702
D)
x 0.9
0.99
0.999
1.001
1.01
1.1
; limit = 2.13640
f(x) 2.15293 2.13799 2.13656 2.13624 2.13481 2.12106
88) If f(x) =

x
f(x)

x - 2, find

3.9

lim f(x).

x→4

3.99

3.999

88)

4.001

4.01

4.1

A)
x 3.9
3.99
3.999
4.001
4.01
4.1
; limit = 1.50
f(x) 1.47736 1.49775 1.49977 1.50022 1.50225 1.52236
B)
x
3.9
3.99
3.999
4.001
4.01

4.1
; limit = 0
f(x) -0.02516 -0.00250 -0.00025 0.00025 0.00250 0.02485
C)
x 3.9
f(x) 3.9000

3.99
2.9000

3.999
1.9000

4.001
4.01
4.1
; limit = ∞
2.0000 3.0000 4.0000

x 3.9
f(x) 3.9000

3.99
2.9000

3.999
1.9000

4.001
4.01

4.1
; limit = 1.95
2.0000 3.0000 4.0000

D)

20


For the function f whose graph is given, determine the limit.
89) Find lim f(x) and
lim f(x).
x→-1 x→-1 +

89)

y
4
2
-6

-4

-2

2

6 x

4

-2
-4
-6
-8
-10

A) -7; -5
90) Find

B) -5; -2

lim f(x) and
x→2 -

C) -7; -2

lim f(x).
x→2 +

90)

y
8
6
4
2
-4

-3

-2

-1

1

2

3

4

D) -2; -7

x

-2
-4
-6
-8

B) 4; -1
D) 1; 1

A) does not exist; does not exist
C) -1; 4

21

91) Find lim f(x).
x→2 -

91)

f(x)
8
7
6
5
4
3
2
1
-2

-1

1

2

3

4

5

6

7

x

-1

A) -1

B) 4

C) 1.3

D) 2.3

92) Find lim f(x).
x→1 -

92)

5

f(x)

4
3
2
1
-5

-4

-3

-2

-1

1

2

3

4

5 x

-1
-2
-3
-4
-5

A) 2

B)

1
2

C) -1

22

D) does not exist


93) Find lim f(x).
x→1 +

93)
5

f(x)

4
3
2
1
-5

-4

-3

-2

-1

1

2

3

4

5 x

-1
-2
-3
-4
-5

A) does not exist

B) 4

C) 3

1
2

D) 3

94) Find lim f(x).
x→0

94)
5

y

4
3
2
1
-5

-4

-3

-2

-1

1

2

3

4

5 x

-1

-2
-3
-4
-5

A) does not exist

B) 0

C) 1

23

D) -1


95) Find lim f(x).
x→0

95)
5

y

4
3
2
1
-5

-4

-3

-2

-1

1

2

3

4

5 x

-1
-2
-3
-4
-5

A) does not exist

C) -1

B) 1

D) 0

96) Find lim f(x).
x→0

96)

8
7
6
5
4
3
2
1
-8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8

A) -3

y

1 2 3 4 5 6 7 8 x

B) does not exist

C) 0

24

D) 3


97) Find lim f(x).
x→-1

97)
y
4

2
A
-4

-2

2

4

x

-2

-4

A) does not exist

B)

2
3

C) -

2
3

D) -1

98) Find lim f(x).
x→-∞

98)
5

f(x)

4
3
2
1
-5

-4

-3

-2

-1

1

2

3

4

5 x

-1
-2
-3
-4
-5

A) -2

B) 0

C) does not exist

D) -∞

Find the limit.
99)

1
lim
x→-2 x + 2
A) 1/2

100)

C) -∞

B) Does not exist

D) ∞

1
lim
x
+9
x → -9 A) -1

101)

99)

100)

C) ∞

B) 0

D) -∞

1
lim
2
x → 10+ (x - 10)
A) -1

101)
B) ∞

C) 0

25

D) -∞