Calculus for scientists and engineers 1st edition briggs test bank
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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 + 6x, [6, 9]
A) 21
2) y = 3x3 - 8x2 + 6, [-8, 5]
181
A)
13
1)
B) 15
C) 45
D) 7
B) 171
2223
C)
5
181
D)
5
C) 2
3
D) 10
2)
3) y =
2x, [2, 8]
1
A)
3
4) y =
3)
B) 7
3
, [4, 7]
x-2
A)
4)
1
3
5) y = 4x2 , 0,
B) -
3
10
C) 2
D) 7
7
4
5)
A) 2
B)
1
3
C) -
3
10
D) 7
6) y = -3x2 - x, [5, 6]
A) -34
7) h(t) = sin (4t), 0,
A)
A)
B) -
4
π
1
6
C) -2
D)
1
2
π
8
8
π
8) g(t) = 3 + tan t, -
6)
7)
B) -
8
π
C)
π
8
D)
4
π
π π
,
4 4
8)
B) -
8
5
C) 0
1
D) -
4
π
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) 2
B) 0.5
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
10)
B) 0.5
C) 1.5
D) 2
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) 4
11)
B) 2
C) 6
2
D) 8
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) 4
12)
B) 8
C) 0
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
13)
B) -0.5
C) 1
D) 0.5
C) slope is -39
1
D) slope is
20
Find the slope of the curve for the given value of x.
14) y = x2 + 5x, x = 4
4
A) slope is 25
15) y = x2 + 11x - 15, x = 1
4
A) slope is 25
16) y = x3 - 5x, x = 1
A) slope is -3
14)
B) slope is 13
15)
1
B) slope is
20
C) slope is 13
D) slope is -39
16)
B) slope is 1
C) slope is 3
D) slope is -2
17) y = x3 - 3x2 + 4, x = 1
A) slope is 0
B) slope is --3
C) slope is -3
D) slope is 1
18) y = 2 - x3 , x = 1
A) slope is 0
B) slope is -3
C) slope is -1
D) slope is 3
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) I
20) Given
B) none
C) II
D) III
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) II
C) III
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) II and III only
B) III and IV only
C) I and II only
21)
D) I and IV 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) 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).
C) 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.
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
B) -
3
4
6 x
-1
A) -1
C) ∞
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) does not exist
C) -3
B) 3
5
D) 0
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) does not exist
B) 3
C) 0
D) -3
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) does not exist
C) -1
B) 0
6
D) 6
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
C) -1
B) does not exist
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) does not exist
B) -1
C) ∞
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) 0
C) does not exist
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) 0
B) does not exist
C) 1
8
D) -2
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
A) -2
32) Find
B) does not exist
C) 2
D) -1
lim f(x) and
lim
f(x)
x→(-1)x→(-1)+
32)
y
2
-4
-2
2
4
x
-2
-4
-6
A) -7; -2
B) -2; -7
C) -7; -5
9
D) -5; -2
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 = 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 = 4.0
f(x) 3.97484 3.99750 3.99975 4.00025 4.00250 4.02485
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) -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
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) -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)
36) Let f(x) =
x
f(x)
x-3
x2 + 2x - 15
, find lim f(x).
x→3
2.9
2.99
2.999
36)
3.001
3.01
3.1
A)
x
2.9
2.99
2.999 3.001
3.01
3.1 ; limit = 0.125
f(x) 0.1266 0.1252 0.1250 0.1250 0.1248 0.1235
B)
x
2.9
2.99
2.999
3.001
3.01
3.1
; limit = -0.125
f(x) -0.1266 -0.1252 -0.1250 -0.1250 -0.1248 -0.1235
C)
x
2.9
2.99
2.999 3.001
3.01
3.1 ; limit = 0.025
f(x) 0.0266 0.0252 0.0250 0.0250 0.0248 0.0235
D)
x
2.9
2.99
2.999 3.001
3.01
3.1 ; limit = 0.225
f(x) 0.2266 0.2252 0.2250 0.2250 0.2248 0.2235
11
37) Let f(x) =
x
f(x)
x2 - 5x + 4
, find lim f(x).
x2 - 6x + 5
x→1
0.9
0.99
37)
0.999
1.001
1.01
1.1
A)
x
0.9
0.99
0.999 1.001
1.01
1.1 ; limit = 0.75
f(x) 0.7561 0.7506 0.7501 0.7499 0.7494 0.7436
B)
x
0.9
0.99
0.999 1.001
1.01
1.1 ; limit = 0.65
f(x) 0.6561 0.6506 0.6501 0.6499 0.6494 0.6436
C)
x
0.9
0.99
0.999 1.001
1.01
1.1 ; limit = 0.8333
f(x) 0.8361 0.8336 0.8334 0.8333 0.8331 0.8305
D)
x
0.9
0.99
0.999 1.001
1.01
1.1 ; limit = 0.85
f(x) 0.8561 0.8506 0.8501 0.8499 0.8494 0.8436
38) Let f(x) =
x
f(x)
sin(6x)
, find lim f(x).
x
x→0
-0.1
-0.01
5.99640065
-0.001
38)
0.001
0.01
5.99640065
A) limit = 6
C) limit = 5.5
39) Let f(θ) =
0.1
B) limit does not exist
D) limit = 0
cos (6θ)
, find lim f(θ).
θ
θ→0
x
-0.1
f(θ) -8.2533561
-0.01
-0.001
39)
0.001
0.01
0.1
8.2533561
B) limit = 6
D) limit = 8.2533561
A) limit does not exist
C) limit = 0
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.
lim g(x)
x→a
g(x)
M
A) 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
41)
f(a) ≠ 0.
lim g(x)
x→a
g(x)
M
B) If lim g(x) = M and lim f(x) = L, then lim
=
= , provided that
lim f(x)
L
x→a
x→a
x→a f(x)
x→a
L ≠ 0.
g(x) g(a)
C) lim
.
=
f(a)
x→a f(x)
g(x) g(a)
D) lim
, provided that f(a) ≠ 0.
=
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 sum or the difference of two functions is the sum of two limits.
B) The limit of a sum or a difference is the sum or the difference of the functions.
C) The limit of a sum or a difference is the sum or the difference of the 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 a constant is continuous.
B) The limit of a product is the product of the limits, and the limit of a quotient is the quotient of
the limits.
C) The limit of a constant is the constant, and the limit of a product is the product of the limits.
D) The limit of a function is a constant times a limit, and the limit of a constant is the constant.
Find the limit.
44) lim
x→7
10
A) 7
44)
B)
7
C)
10
D) 10
45) lim (9x - 4)
x→1
A) -5
46)
45)
B) -13
C) 5
D) 13
lim (15 - 2x)
x→-18
A) 21
43)
46)
B) -21
C) 51
13
D) -51
Give an appropriate answer.
47) Let lim f(x) = 5 and lim g(x) = -8. Find lim [f(x) - g(x)].
x→9
x→9
x→9
A) 9
48) Let
B) 13
B) -4
C) -36
48)
D) 4
f(x)
lim f(x) = 9 and lim g(x) = -4. Find lim
.
g(x)
x → -9
x → -9
x → -9
A) -
50) Let
D) -3
lim f(x) = -9 and lim g(x) = 4. Find lim [f(x) ∙ g(x)].
x → -4
x → -4
x → -4
A) -5
49) Let
C) 5
47)
4
9
B) -9
lim f(x) = 16. Find lim
x → -2
x → -2
A) 2.0000
C) 13
49)
D) -
9
4
f(x).
50)
B) -2
C) 4
D) 16
51) Let lim f(x) = 1 and lim g(x) = -7. Find lim [f(x) + g(x)]2 .
x→1
x→1
x→1
A) 50
B) -6
52) Let lim f(x) = 243. Find lim
x→6
x→6
A) 3
5
C) 8
52)
B) 6
14
3
D) 36
f(x).
C) 5
53) Let lim f(x) = -8 and lim g(x) = 6. Find lim
x→ 1
x→ 1
x→ 1
A) -
51)
D) 243
6f(x) - 10g(x)
.
-9 + g(x)
B) 1
C) 36
53)
D) - 4
Find the limit.
54) lim (x3 + 5x2 - 7x + 1)
x→2
A) 0
55)
B) does not exist
C) 29
D) 15
lim (3x5 - 3x4 - 4x3 + x2 + 5)
x→-2
A) -7
56)
54)
55)
B) -167
C) 41
D) -103
x
lim
3x
+2
x→-1
A) 1
56)
B) -
1
5
C) 0
14
D) does not exist
57) lim
x→0
x3 - 6x + 8
x-2
A) -4
57)
B) 0
C) Does not exist
D) 4
3x2 + 7x - 2
58) lim
x→1 3x2 - 4x - 2
A) Does not exist
59)
58)
B) -
7
4
C) 0
D) -
8
3
lim (x + 3)2 (x - 1)3
x→-2
A) -675
60) lim
x→7
B) -1
C) -27
D) -25
x2 + 4x + 4
A) 81
61) lim
x→5
59)
60)
B) ±9
C) 9
D) does not exist
7x + 51
A) -86
62) lim
h→0
61)
B)
C) - 86
86
D) 86
2
3h + 4 + 2
A) 1
63) lim
x→0
A) 1/2
62)
B) 2
C) 1/2
D) Does not exist
1+x-1
x
63)
B) Does not exist
C) 1/4
D) 0
Determine the limit by sketching an appropriate graph.
for x < 1
64) lim f(x), where f(x) = -3x + 4
5x
5
for x ≥ 1
+
x → 1A) 1
65)
66)
B) 6
lim f(x), where f(x) = -2x + 2
4x + 3
x → 6+
A) -10
C) 5
D) 10
for x < 6
for x ≥ 6
65)
B) 4
2
lim f(x), where f(x) = x + 4
0
x → 4+
A) 0
64)
C) 27
D) 3
for x ≠ 4
for x = 4
66)
B) 12
C) 16
15
D) 20
67)
lim f(x), where f(x) =
x → 1A) 4
68)
lim f(x), where f(x) =
x → -7 +
A) Does not exist
1 - x2
1
4
B) 1
x
1
0
B) -7
0≤x<1
1≤x<4
x=4
67)
C) 0
D) Does not exist
-7 ≤ x < 0, or 0 < x ≤ 1
x=0
x < -7 or x > 1
C) -0
68)
D) 6
Find the limit, if it exists.
x3 + 12x2 - 5x
69) lim
5x
x→0
A) -1
69)
B) 0
C) Does not exist
D) 5
x4 - 1
70) lim
x→1 x - 1
A) 0
71)
B) 2
lim
x → -5
lim
x→7
lim
x→2
B) 4
C) 2
D) 1
72)
B) 2
C) 120
D) 12
73)
B) 3
C) 17
D) Does not exist
x2 + 2x - 8
x2 - 4
A) Does not exist
75)
71)
x2 + 3x - 70
x-7
A) 0
74)
D) 4
x2 + 12x + 35
x+5
A) Does not exist
73)
C) Does not exist
x2 - 4
lim
x→2 x-2
A) Does not exist
72)
70)
74)
B) 0
C)
3
2
D) -
1
2
x2 - 4
lim
2
x → 2 x - 7x + 10
A) -
4
3
75)
C) -
B) 0
16
2
3
D) Does not exist
x2 - 9x + 18
76) lim
x→6 x2 - 3x - 18
76)
B) -
A) 1
77)
lim
h→0
lim
x → 10
C)
1
3
D) Does not exist
(x + h)3 - x3
h
A) 0
78)
1
3
77)
C) 3x2 + 3xh + h2
B) Does not exist
D) 3x2
10 - x
10 - x
78)
A) Does not exist
C) -1
B) 0
D) 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) 0.0007
80) The inequality 1Find lim
x→0
A) 1
B) 0
C) does not exist
D) 1
x2 sin x
<
< 1 holds when x is measured in radians and x < 1.
2
x
sin x
if it exists.
x
B) 0.0007
C) does not exist
D) 0
81) If x3 ≤ f(x) ≤ x for x in [-1,1], find lim f(x) if it exists.
x→0
A) -1
80)
B) 1
81)
C) does not exist
17
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
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 = 18.0
f(x) 16.810 17.880 17.988 18.012 18.120 19.210
C)
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
D)
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
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
A)
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
B)
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
C)
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
D)
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
18
1.1
84) If f(x) =
x3 - 6x + 8
, find lim f(x).
x-2
x→0
-0.1
x
f(x)
-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 = -1.20
f(x) -1.22843 -1.20298 -1.20030 -1.19970 -1.19699 -1.16858
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 = -2.10
f(x) -2.18529 -2.10895 -2.10090 -2.99910 -2.09096 -2.00574
D)
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
85) If f(x) =
x
f(x)
x-4
, find lim f(x).
x-2
x→4
3.9
3.99
3.999
85)
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 = ∞
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 = 4.0
f(x) 3.97484 3.99750 3.99975 4.00025 4.00250 4.02485
D)
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
19
86) If f(x) = x2 - 5, find
-0.1
x
f(x)
lim f(x).
x→0
86)
-0.01
-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 = -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
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
B)
C)
D)
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 = 0.21213
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 = 2.13640
f(x) 2.15293 2.13799 2.13656 2.13624 2.13481 2.12106
D)
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
20
88) If f(x) =
x
f(x)
x - 2, find
3.9
lim f(x).
x→4
3.99
88)
3.999
4.001
4.01
4.1
A)
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
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
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
D)
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
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
4
6 x
-2
-4
-6
-8
-10
A) -5; -2
B) -7; -2
C) -7; -5
21
D) -2; -7
90) Find
lim f(x) and
x→2 -
lim f(x).
x→2 +
90)
y
8
6
4
2
-4
-3
-2
-1
1
2
3
x
4
-2
-4
-6
-8
A) 1; 1
C) -2; 4
B) does not exist; does not exist
D) 4; -2
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) 2.3
C) 1.3
22
D) 4
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)
1
2
B) does not exist
C) 2
D) -1
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) 3
B) 3
1
2
C) 4
23
D) does not exist
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) -3
B) does not exist
C) 0
D) 3
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) -1
B) 0
C) does not exist
D) 1
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) -4
y
1 2 3 4 5 6 7 8 x
B) 0
C) 4
24
D) does not exist
97) Find lim f(x).
x→-1
97)
y
4
2
A
-4
-2
2
4
x
-2
-4
A)
1
2
1
2
B) -
C) -1
D) does not exist
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) 0
C) -2
B) does not exist
D) -∞
Find the limit.
99)
1
lim
x→-2 x + 2
A) Does not exist
100)
B) -∞
C) ∞
D) 1/2
1
lim
x
+4
x → -4 A) -∞
101)
99)
100)
B) -1
C) 0
D) ∞
1
lim
2
x → 10+ (x - 10)
A) 0
101)
B) ∞
C) -∞
25
D) -1
