Limits and Their PropertiesChapter 19667. Using tIntermedi42. lim 3/x-3 x 341. limx-5x-25+ x 25f (x) = 2(x- 2)2, x 243. lim f(x), where f(x) =x2has a zerCx > 22 x,68. Using tIntermedi.1 - x, xs 144. lim g(x), where g(x)x > 1x + 1,x1+f(x) = x2+ 1, t2s24s+6,s 247. lim (2x] +1)48. lim [x 1to the indicatx2x-4the theorem.x2-450. lim x(x- 1)49. limx-2x- 269. f(x) = x2x-1+70. f(x) = (xContinuity on a Closed Interval In Exercises 51 and 52,discuss the continuity of the function ca he cloged interval.XDeterminindetermine wh51. g(x) = 8 -, [-2, 2]M6 from the lefRemovable and Nonremovable Discontinuities InExercises 53-58, find the x-values (if any) at which f is notcontinuous. Which of the discontinuities are removable?71. f(x) =xFinding Vethe vertical as53. f(x) x-8 1x54. f(x) x2x + 20455. fx)x51 =56. f(x)2- 9373. f(x) =x57. flx) =Xx+3He58. f(x) x- 3x- 18x3- x75. f(x) =59. Making a Function Continuous Find the value of csuch that the function is continuous on the entire real number277. f(x) = seline.Finding a Oflx) =x+3, x2lcx + 6, x> 2Xone-sided limi60. Making a Functi

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Asked Sep 15, 2019

Solve 51

Limits and Their Properties
Chapter 1
96
67. Using t
Intermedi
42. lim 3/
x-3 x 3
41. limx-5
x-25+ x 25
f (x) = 2
(x- 2)2, x 2
43. lim f(x), where f(x) =
x2
has a zerC
x > 2
2 x,
68. Using t
Intermedi.
1 - x, xs 1
44. lim g(x), where g(x)
x > 1
x + 1,
x1+
f(x) = x2
+ 1, t<1
2t1), t 1
45. lim h(t), where h(t)
has at leas
+
t-1
s-2
- s2 - 4s 2,
Using the
69 and 70, ve
46. lim f(s), where f(s)
s >2
s24s+6,
s 2
47. lim (2x] +1)
48. lim [x 1
to the indicat
x2
x-4
the theorem.
x2-4
50. lim x(x- 1)
49. lim
x-2
x- 2
69. f(x) = x2
x-1+
70. f(x) = (x
Continuity on a Closed Interval In Exercises 51 and 52,
discuss the continuity of the function ca he cloged interval.
X
Determinin
determine wh
51. g(x) = 8 -, [-2, 2]
M
6 from the lef
Removable and Nonremovable Discontinuities In
Exercises 53-58, find the x-values (if any) at which f is not
continuous. Which of the discontinuities are removable?
71. f(x) =
x
Finding Ve
the vertical as
53. f(x) x-8 1x
54. f(x) x2
x + 20
4
55. fx)x5
1 =
56. f(x)2- 9
3
73. f(x) =
x
57. flx) =
X
x+3
He58. f(x) x- 3x- 18
x3- x
75. f(x) =
59. Making a Function Continuous Find the value of c
such that the function is continuous on the entire real number
2
77. f(x) = se
line.
Finding a O
flx) =x+3, x2
lcx + 6, x> 2
X
one-sided limi
60. Making a Functi
help_outline

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Limits and Their Properties Chapter 1 96 67. Using t Intermedi 42. lim 3/ x-3 x 3 41. limx-5 x-25+ x 25 f (x) = 2 (x- 2)2, x 2 43. lim f(x), where f(x) = x2 has a zerC x > 2 2 x, 68. Using t Intermedi. 1 - x, xs 1 44. lim g(x), where g(x) x > 1 x + 1, x1+ f(x) = x2 + 1, t<1 2t1), t 1 45. lim h(t), where h(t) has at leas + t-1 s-2 - s2 - 4s 2, Using the 69 and 70, ve 46. lim f(s), where f(s) s >2 s24s+6, s 2 47. lim (2x] +1) 48. lim [x 1 to the indicat x2 x-4 the theorem. x2-4 50. lim x(x- 1) 49. lim x-2 x- 2 69. f(x) = x2 x-1+ 70. f(x) = (x Continuity on a Closed Interval In Exercises 51 and 52, discuss the continuity of the function ca he cloged interval. X Determinin determine wh 51. g(x) = 8 -, [-2, 2] M 6 from the lef Removable and Nonremovable Discontinuities In Exercises 53-58, find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? 71. f(x) = x Finding Ve the vertical as 53. f(x) x-8 1x 54. f(x) x2 x + 20 4 55. fx)x5 1 = 56. f(x)2- 9 3 73. f(x) = x 57. flx) = X x+3 He58. f(x) x- 3x- 18 x3- x 75. f(x) = 59. Making a Function Continuous Find the value of c such that the function is continuous on the entire real number 2 77. f(x) = se line. Finding a O flx) =x+3, x2 lcx + 6, x> 2 X one-sided limi 60. Making a Functi

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check_circleExpert Solution
Step 1

Consider the given function and closed interval.

g(x)- -x-2,2]
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g(x)- -x-2,2]

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Step 2

For p in (-2, 2) So,

lim f (x) f(p)
x-p
f(p) lim8-x
xp
So, function is continous on [-2,2].
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lim f (x) f(p) x-p f(p) lim8-x xp So, function is continous on [-2,2].

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Step 3

Similarly...

lim f(p) (2)
x-2
and
lim f(p) f(2)
x3
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lim f(p) (2) x-2 and lim f(p) f(2) x3

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