Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)
10th Edition
ISBN: 9781305657861
Author: Soo T. Tan
Publisher: Cengage Learning
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Chapter B, Problem 10E
To determine
To evaluate: The value of
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In Exercises 75–78, sketch the graph of a function y = f(x) that satis-
fies the given conditions. No formulas are required-just label the
coordinate axes and sketch an appropriate graph. (The answers are not
unique, so your graphs may not be exactly like those in the answer
section.)
75. f(0) = 0, f(1) = 2, f(-1) = -2, lim f(x) = -1, and
x--00
lim f(x) = 1
76. f(0) = 0, lim f(x) = 0, lim f(x) = 2, and lim f(x) = -2
x→0*
%3D
77. f(0) = 0, lim f(x) = 0, lim f(x) = lim f(x) = ∞,
x-too
x→1-
x--1+
= -0, and lim f(x) = -∞
lim f(x)
x→1*
78. f(2) = 1, f(-1) = 0, lim f(x) = 0, lim f(x) = ∞,
x→0*
lim f(x) = -00, and lim f(x) = 1
X -00
Find the limits in Exercises 33–35 Are the functions continuous at the point being approached?
Divide numerator and denominator by the highest power of x in the
denominator and proceed from there. Find the limits in Exercises 23–36.
8x² – 3
1/3
x² +
8x2 – 3
23. lim
x→0 V 2x? + x
24. lim
x--00
\5
x² – 5x
25. lim
x→-ox2 + 7x
26. lim
x→ o Vx + x – 2
2Vx + x!
2 + Vx
27. lim
28. lim
x00 2 - Vx
Зх — 7
Vx – Vĩ
VI + Vĩ
x' + x4
29. lim
30. lim
x→-00
VI
lim
32.
x--0 2x + x²/3 – 4
2x/3 – x'/3 + 7
5x + 3
31. lim
x-00 8/5 + 3x + Vx
Vx² + 1
Vx² + 1
33. lim
x00 x + 1
34. lim
x→-0 x + 1
4 - 3x3
lim
35. lim
x→∞ V4x? + 25
36.
x→-0 Vx6 + 9
Chapter B Solutions
Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)
Ch. B - Prob. 1ECh. B - Prob. 2ECh. B - Prob. 3ECh. B - Prob. 4ECh. B - Prob. 5ECh. B - Prob. 6ECh. B - Prob. 7ECh. B - Prob. 8ECh. B - Prob. 9ECh. B - Prob. 10E
Ch. B - Prob. 11ECh. B - Prob. 12ECh. B - Prob. 13ECh. B - Prob. 14ECh. B - Prob. 15ECh. B - Prob. 16ECh. B - Prob. 17ECh. B - Prob. 18ECh. B - Prob. 19ECh. B - Prob. 20ECh. B - Prob. 21ECh. B - Prob. 22ECh. B - Prob. 23ECh. B - Prob. 24ECh. B - Prob. 25ECh. B - Prob. 26ECh. B - Prob. 27ECh. B - Prob. 28ECh. B - Prob. 29ECh. B - Prob. 30ECh. B - Prob. 31ECh. B - Prob. 32ECh. B - Prob. 33ECh. B - Prob. 34E
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- For the function f graphed as follows, approximate each of the limits and values in Exercises 31–34: 3 1. + + -4 -3 -2/-1 1 2 4 -2- 31. lim f(x), lim f(x), lim_f(x), and f(-2). X-2- X-2+" X-2 32. lim f(x), lim f(x), lim f(x), and f(-1). x-1-* X-1+ X-1 33. lim f(x), lim f(x), lim f(x), and f(2). X2- x+2+ X+2 34. lim f(x), lim f(x), lim f(x), and lim f(x). x-00 3.arrow_forwardIn Exercises 11–50, evaluate the limit if it exists. If not, determine whether the one-sided limits exist. For limits that don't exist indicate whether they can be expressed as = -o or = ∞.arrow_forwardUse formal definitions to prove the limit statements in Exercises 95–98. -1 95. lim 96. lim x→0 x -2 98. lim x→-5 (x + 5)² 97. lim x→3 (x 3)2 ||arrow_forward
- L'Hôpital’s Rule does not help with the limits in Exercises 67–74. Try it-you just keep on cycling. Find the limits some other way. Vx V9x + 1 67. lim x→0 Vx + 1 68. lim x-0* Vsinx cot x sec x 70. lim x0* csc x 69. lim x→(7/2)- tan x 2* 71. lim 3* 2* + 4* 72. lim x00 5* – 2* 3* + 4* х 74. lim x→0* e¯l/x lim 73.arrow_forwardFind the limits in Exercises 125–132. sin x 3x – tan 7x 125. lim x0 2x? – x 126. lim 2x x→0 sin (sin 0) sin r 127. lim 128. lim 0 tan 2r 4 tan? 0 + tan 0 lim + 1 129. tan² 0 + 5 0→(T/2) – 2 cot? 0 1 130. lim 60* 5 cot? 0 – 7 cot 0 – 8 1 - cos 0 02 x sin x 131. lim x→0 2 – 2 cos x 132. lim 0→0arrow_forwardFind the limits in Exercises 37–48. 5 38. lim 37. lim x→0* 3x 3 39. lim 40. lim 3 x→3* X 2x Зх 42. lim x--5 2x + 10 41. lim x→-8* x + 8 -1 43. lim x-7 (x – 7)2 44. lim x>0 x(x + 1) 2 45. a. lim x→0* 3x'/3 b. lim x->0 3x'/3 2 46. a. lim x→0* x!/5 b. lim x→0 x!/5 4 47. lim x→0 x²/5 48. lim x→0 r2/3arrow_forward
- The process by which we determine limits of rational functions applies equally well to ratios containing noninteger or negative powers of x: Divide numerator and denominator by the highest power of x in the denominator and proceed from there. Find the limits in Exercises 23–36.arrow_forwardFind the limits in Exercises 49–52. 49. x→(7/2) lim tan x 50. x>(-7/2)* lim sec x 51. lim (1 + csc 0) lim (2 – cot 0) 52. 0→0 0→0arrow_forwardEvaluate lim,0+ e(1/z) .arrow_forward
- Evaluate the limits in Exercises 55–60. Use the theorems in this section to justify each step of your work. 55. lim k→o 2k sin k (Hint: Use the Squeeze Theorem.) (1+:)(--}) 56. lim k00 k – 7 k3 +1 57. lim k00 3k +5 58. lim k2 59. lim (Vk2 + k – k) 60. lim (Vk3 +k+1 - vk3 – k – 1) (Hint: Write as a quo- k00 tient and rationalize the numerator.)arrow_forwardIn Exercises 29–32, find the limit of g(x) as x approaches the indicated value. 29. lim (4g(x))'/3 = 2 x→0* 30. lim xV5 x + g(x) 2 3x2 + 1 31. lim g(x) 5 - x? 32. 32. lim x--2 Vg(x)arrow_forwardIn Exercises 79–82, find a function that satisfies the given conditions and sketch its graph. (The answers here are not unique. Any function that satisfies the conditions is acceptable. Feel free to use formulas defined in pieces if that will help.) 79. lim f(x) = 0, lim f(x) = ∞, and lim f(x) = ∞ x→too x-2+ 80. lim g(x) = 0, lim g(x) = –∞, and lim g(x) = ∞ x→3- x→3* 81. lim h(x) = -1, lim h(x) = 1, lim h(x) = -1, and x -00 lim h(x) = 1 x→0+ 1, lim k(x) x→l¯ = 00, and lim k(x) x→I* 82. lim k(x) = -00arrow_forward
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