# MATH 101 Week 1 Derivatives Question

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2:24 PM Mon Sep 28
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(a = 0)
3x
x – x
51. lim
.
2.x2
52. lim
X
18. f(x)
Sx-1 if x < 3 - 2x + 8 if x > 3
(a = 3)
x2 – 25
53. lim
—5x + 5
b + 1
54. lim
–3b + 3
X
19. f(x)
if x < 1 if x = 1 if x > 1
0
-X + 2
(a = 1)
X
55. lim
2-3-1
x + 2
56. lim
2+28 – 2
– x – 6
57. lim
*–2x + x – 2
58. lim
20. f(x)
– 8
2.
– 2x + 4 if x 1
Slxl if x = 0
(a = 0)
1 if x = 0
X-4
60. lim
3-4 VX-2
21. f(x)
Vr-1
59. lim
1-X-1
Vx+1
Hint: Multiply by
Vx+1
=
Hint: See Exercise 59.
x – 1|
22. f(x)
{
if x # 1
if x = 1
(a = 1)
X-1
61. lim
*- x + x2 – 2x
4 – x2
62. lim
-~-2 2×2 + x3
In Exercises 23-40, find the indicated limit.
23. lim 3
24. lim -3
X-2
In Exercises 63-68, use the graph of the function f to determine
lim f(x) and lim f(x), if they exist.
X2
25. lim x
26. lim – 3x
–2
63.
64.
AY
f(x) = 2×2 – 10
f(x) = x3 – x
27. lim (1 – 2x)
28. lim (412 – 2t + 1)
29. lim (2x – 3×2 + x + 2)
10
30. lim (4×5 – 20×2 + 2x + 1)
-1
1 2 3
10
3
31. lim (2s2 – 1)(2s + 4) 32. lim (x2 + 1)(x2 – 4)
3-0
x2
65.
66.
2x + 1
33. lim
*2 x + 2
x2
x3 + 1
34. lim
– 2×3 + 2
36. lim V 5x + 2
1-2
35. lim Var + 2
f(x) =
1
37. lim V2x4 + x2
38. lim
x-12
121² + 4
x? + 1
-3 -2 -1
-2
1
2
メ→-3
3
67.
AY
V x2 + 8
39. lim
*–1 2x + 4
XV x2 + 7
40. lim
**3 2x – 2x + 3
f(x) = 2 – 4
3
In Exercises 41-48, find the indicated limit given that
lim f(x) = 3 and lim g(x) = 4.
A
X
-1
41. lim (f(x) – g(x)]
42. lim 2f(x)
43. lim (2f(x) – 3g(x)]
44. lim [f(x)g(x)]
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2:25 PM Mon Sep 28
100%
< AA chegg.com + X Chegg eReader Chegg eReader: Applied Mathematics for the Manageri... < Q 610 CHAPTER 9 THE DERIVATIVE 68. y 81. Toxic WASTE A city's main well was recently found to be contaminated with trichloroethylene, a cancer-causing chem- ical, as a result of an abandoned chemical dump leaching chemicals into the water. A proposal submitted to city coun- cil members indicates that the cost, measured in millions of dollars, of removing x% of the toxic pollutant is given by 1 V-X SV- if x < 0 f(x) = x if x > 0
-2 – 1
1
2
3
x + 1
C(x)
0.5x
100 – x
(0

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