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 13E
To determine
To evaluate: The value of
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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
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 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→0
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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Find the limits in Exercises 13–20. (If in doubt, look at the function's graph.) 14. lim cos!x 13. lim sinx x→I- 15. lim tan-x 17. lim sec-lx 16. lim tan 18. lim sec-lx 19. lim csc¬lx 20. lim csc-lxarrow_forwardFor 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_forwardL'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_forward
- Find 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_forwardUse calculator graphs to make approximations for each of the limits in Exercises 67–74. 67. lim(3 – 4x - 5x²) 68. lim (–0.2r5 + 100x) X4 x00 3 — х 69. lim x→1 x – 1 x+1 70. lim x2 x - 2 x100 71. lim Inx 72. lim X00 X 1- cosx sinx 73. lim X0 X 74. limarrow_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
- Show that lim x|cos = 0.arrow_forwardFind the limits in Exercises 125–132. sin x 3x 126. lim- tan 7x 125. lim 0 2r 2x sin r sin (sin 0) 127. lim 128. lim o tan 2r 4 tan? 0 + tan 0 + 1 129. lim (/2) tan 0 + 5 1- 2cot 0 80 5 cot? 0 - 7 cot 0 - 8 130. lim x sin x 2 - 2 cos x cos 0 131. lim 132. limarrow_forwardIn Exercises 3–8, find the limit of each function (a) as x→∞ and (b) as x→ -. (You may wish to visualize your answer with a graphing calculator or computer.) 2 4. f(x) = 7 x² 3. f(x) = 3 5. g(x) 6. g(x) 8 – (5/x²) 2 + (1/x) -5 + (7/x) 3 - (1/x²) 3 - (2/x) 7. h(x) 8. h(x) 4 + (V2/x²)arrow_forward
- What does the limit notation lim f(x) = L mean? Xa"arrow_forwardThe 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_forwardIn Exercises 7–10, use the formal definition of limit to prove that the function is continuous at c.arrow_forward
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