xe* 33. lim e-3r 35. lim 1+00 x+ 3x+1 log, x 37. lim X+0+ log, 3x In(x – 2) 39. lim In(x² – 4) X+2+ COS X – 1 41. lim 1→0 sin x - 1- COS X 43. lim tan x

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Chapter1: Functions And Models
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# 33, 39, 43 please
Calculate each of the limits in Exercises 21-48. Some of these
limits are made easier by L'Hôpital's rule, and some are not.
Transcribed Image Text:Calculate each of the limits in Exercises 21-48. Some of these limits are made easier by L'Hôpital's rule, and some are not.
Calculate each of the limits in Exercises 49-64. Some of these
limits are made easier by considering the logarithm of the
limit first, and some are not.
dominates la
32. lim
x→00 x2 + 3x +1
Xe-3x
31. lim x
オ→0
65. u(x) =
66. u(x) =
34. lim
2* – 1
33. lim
67. u(x) =
X→0+
x2
e 3x
68. u(x) :
ex
In x
35. lim
100 x2 + 3x + 1
36. lim
x→00 In(2x + 1)
69. u(x) =
70. u(x) =
log, x
log, 3x
2x
38. lim In
- 4
37. lim
71. u(x) =
X2+
X- 2
72. u(x) =
In(x – 2)
Inx
39. lim
X+2+
40. lim
x→0+ lnx – x +1
73. и() -
In(x2 – 4)
74. u(x) = |
COS X –
- 1
sin x
41. lim
42. lim
x0 x+ sinx
As you will -
functions ek
functions x"
mic functions
of the limits
sin x
1- cos x
43. lim
sin(cos x)
lim
x>7/2
44.
tan x
COS X
X COS X
sin(In x)
45. lim
x0 1-ex
46. lim
X1 X- 1
75. lim
tan-x
47. lim
tan-x
48. lim
x0 sin-x
X→0 sinx
77. lim
X 300
79. lim 2 x
x+48
49. lim xnx
Now that we
more sophisti
domains, lim.
.Inx
50. lim x
L lim (x- 2)*2-4
52. lim (r2 + 1)*
global extrem
given intervals
81. f(x) =x 1
X2+
53.
lim x/x-1)
X1+
54. lim x
55. lim x/x
()
56.
lim
82. f(x) = x?
83. f(x) = xe
In
X00
408
Transcribed Image Text:Calculate each of the limits in Exercises 49-64. Some of these limits are made easier by considering the logarithm of the limit first, and some are not. dominates la 32. lim x→00 x2 + 3x +1 Xe-3x 31. lim x オ→0 65. u(x) = 66. u(x) = 34. lim 2* – 1 33. lim 67. u(x) = X→0+ x2 e 3x 68. u(x) : ex In x 35. lim 100 x2 + 3x + 1 36. lim x→00 In(2x + 1) 69. u(x) = 70. u(x) = log, x log, 3x 2x 38. lim In - 4 37. lim 71. u(x) = X2+ X- 2 72. u(x) = In(x – 2) Inx 39. lim X+2+ 40. lim x→0+ lnx – x +1 73. и() - In(x2 – 4) 74. u(x) = | COS X – - 1 sin x 41. lim 42. lim x0 x+ sinx As you will - functions ek functions x" mic functions of the limits sin x 1- cos x 43. lim sin(cos x) lim x>7/2 44. tan x COS X X COS X sin(In x) 45. lim x0 1-ex 46. lim X1 X- 1 75. lim tan-x 47. lim tan-x 48. lim x0 sin-x X→0 sinx 77. lim X 300 79. lim 2 x x+48 49. lim xnx Now that we more sophisti domains, lim. .Inx 50. lim x L lim (x- 2)*2-4 52. lim (r2 + 1)* global extrem given intervals 81. f(x) =x 1 X2+ 53. lim x/x-1) X1+ 54. lim x 55. lim x/x () 56. lim 82. f(x) = x? 83. f(x) = xe In X00 408
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