11One-Sided Limits: Continuous Fun4doso q en (n10mx +xx2420. limadnx-x - 1221. lim19. lim2xtion found in Example22. limx2 9x3 123. limx 3xt 1x 324. limx-1 X(x 1)225. lim*1 x 1-1 x 11asx3 x2 +3x + 3x3 x2x- 126. limx 227. limxt-x32x228. limx-1 X X 2x +2x3 2x2+29. limx2 xx2x3-x23x - 3x2 3x-4x3 2x + x30. limx1x332. limx3 x 3x3- 3x2 +the function31. limx-1 X+ x+ 2x + 2In Problems 33-44, find the limit as x approaches c of the average rate of change of each functionfrom c to x.33. c 2; f(x) = 5x - 334. c -2; f(x) = 4-3x35. c 3; f(x)36. c 3; f(x) = x37. c= -1; f(x) = x + 2x38. c -1; f((x - 2)39. c 0; f(x) 3x3 - 2x2 + 440. c 0; f(x) = 4x3- 5x + 841. c 1; f(x- 2142. c 1; f(x) =SOrO43. c 4; f(x) vx44. c 1; f(501 ootx2Jmmsyt pwoll..odIn Problems 45-52, assume that lim f(x) = 5 and lim g(x) = 2 to find each limit.prdegexC45. lim [2f(x)]46. lim [f(x) g(x)]47. lim [g(x)]xcxC350. lim*c g(x)51. lim [4f(x) 5g(x)]2)-7449. lim*c f(x)2ntinuous Functions12.3 On

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Asked Oct 27, 2019
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I need help with number 39

11
One-Sided Limits: Continuous Fun
4doso q en (n10mx +x
x24
20. lim
adnx-x - 12
21. lim
19. lim
2x
tion found in Example
22. lim
x2 9
x3 1
23. lim
x 3
xt 1
x 3
24. lim
x-1 X
(x 1)2
25. lim
*1 x 1
-1 x 1
1
as
x3 x2 +3x + 3
x3 x2x- 1
26. lim
x 2
27. lim
xt-
x32x2
28. lim
x-1 X X 2x +2
x3 2x2
+
29. lim
x2 x
x2
x3-x23x - 3
x2 3x-4
x3 2x + x
30. lim
x1
x3
32. lim
x3 x 3x3
- 3x2 +
the function
31. lim
x-1 X+ x+ 2x + 2
In Problems 33-44, find the limit as x approaches c of the average rate of change of each function
from c to x.
33. c 2; f(x) = 5x - 3
34. c -2; f(x) = 4-3x
35. c 3; f(x)
36. c 3; f(x) = x
37. c= -1; f(x) = x + 2x
38. c -1; f(
(x - 2)
39. c 0; f(x) 3x3 - 2x2 + 4
40. c 0; f(x) = 4x3- 5x + 8
41. c 1; f(x
- 2
1
42. c 1; f(x) =
SOrO
43. c 4; f(x) vx
44. c 1; f(
501 oot
x2
Jmmsyt pwoll..od
In Problems 45-52, assume that lim f(x) = 5 and lim g(x) = 2 to find each limit.
prdege
xC
45. lim [2f(x)]
46. lim [f(x) g(x)]
47. lim [g(x)]
xc
xC
3
50. lim
*c g(x)
51. lim [4f(x) 5g(x)]
2)-7
4
49. lim
*c f(x)
2
ntinuous Functions
12.3 On
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11 One-Sided Limits: Continuous Fun 4doso q en (n10mx +x x24 20. lim adnx-x - 12 21. lim 19. lim 2x tion found in Example 22. lim x2 9 x3 1 23. lim x 3 xt 1 x 3 24. lim x-1 X (x 1)2 25. lim *1 x 1 -1 x 1 1 as x3 x2 +3x + 3 x3 x2x- 1 26. lim x 2 27. lim xt- x32x2 28. lim x-1 X X 2x +2 x3 2x2 + 29. lim x2 x x2 x3-x23x - 3 x2 3x-4 x3 2x + x 30. lim x1 x3 32. lim x3 x 3x3 - 3x2 + the function 31. lim x-1 X+ x+ 2x + 2 In Problems 33-44, find the limit as x approaches c of the average rate of change of each function from c to x. 33. c 2; f(x) = 5x - 3 34. c -2; f(x) = 4-3x 35. c 3; f(x) 36. c 3; f(x) = x 37. c= -1; f(x) = x + 2x 38. c -1; f( (x - 2) 39. c 0; f(x) 3x3 - 2x2 + 4 40. c 0; f(x) = 4x3- 5x + 8 41. c 1; f(x - 2 1 42. c 1; f(x) = SOrO 43. c 4; f(x) vx 44. c 1; f( 501 oot x2 Jmmsyt pwoll..od In Problems 45-52, assume that lim f(x) = 5 and lim g(x) = 2 to find each limit. prdege xC 45. lim [2f(x)] 46. lim [f(x) g(x)] 47. lim [g(x)] xc xC 3 50. lim *c g(x) 51. lim [4f(x) 5g(x)] 2)-7 4 49. lim *c f(x) 2 ntinuous Functions 12.3 On

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Expert Answer

Step 1

Use the average rate formula from c to x. With limit x-> c

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f(x)-f (c) lim X-с 3x3-2x2+4-(3c3-2c2+4) lim X-с х—с

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Step 2

Simplify the expres...

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3x3-2x2+4-(3c3-2c2+4) lim X-с х—с 3x3-2x2+4-3c3+2¢2-4 =lim х—е X-с 3x3-3c3-2x2+2c lim X-с х—с 3(x2-c3)-2(x2-c2) =lim X-с х—с

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