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 24E
To determine
To evaluate: The value of
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Use tables of values to make educated guesses for each of the
limits in Exercises 39–52.
39. lim (x2 + x+ 1)
40. lim (1 – 3x +x²)
x+2-
X3+
1
41. lim
1+2 x2 – 4
1
42. lim
x1 1- x
х — 3
х — 5
43. lim
x-3 (x2 – 2)(x – 3)
44. lim
x+5 x2 – 25
3
45. lim
X+2 4 - 2*
2x
46. lim (Зe + 1)
X00
Зх + 1
1+ 2x
47. lim
X-00 1- r
48. lim
X00 Y -1
x+1
1
+
2x +1
1
49. lim
x-0 x2 - 1
50. lim (1+
X00
51. lim sinx
52. lim sin
x00
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 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-lx
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 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_forwardIn Exercises 7–10, use the formal definition of limit to prove that the function is continuous at c.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_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_forwardEach of Exercises 31–36 gives a function ƒ(x), a point c, and a positivenumber P. Find L = lim xSc ƒ(x). Then find a number d 7 0 suchthat for all x0 < x - c < d => ƒ(x) - L < P. ƒ(x) = -3x - 2, c = -1, P = 0.03arrow_forward
- Find 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_forwardIn Exercises 14 – 15, find: ļim ((x+h) – f(x)' h-0 15. f(x) = vx2- 3arrow_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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