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 26E
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
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
In 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)
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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- 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 -00arrow_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_forwardIn Exercises 14 – 15, find: ļim ((x+h) – f(x)' h-0 15. f(x) = vx2- 3arrow_forward
- In Exercises 7–10, use the formal definition of limit to prove that the function is continuous at c.arrow_forwardFind the limit. 1) lim x-4/ln x x-0+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_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_forwardEvaluate lim,0+ e(1/z) .arrow_forwardUse e-o definition and prove that lim (r-5z)=-6arrow_forward
- Find lim (e-2x cos x) (Hint: Squeeze Theorem)arrow_forwardEvaluate 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 11–20, verify each limit using the limit definition. For ex- ample, in Exercise 11, show that |2x – 6| can be made as small as desired by taking x close to 3. - 11. lim 2x x→3 12. lim 4 = 4 x→3 6 13. lim (4x + 3) = 11 x→2 14. lim (5x – 7) = 8 x→3 %3D 15. lim (-2x) = -18 x→9 16. lim (1 — 2х) — 11 x→-5 17. lim x? = 0 18. lim (2x2 +4) = 4 x→0 x→0 19. lim (x2 + 2x + 3) = 3 x→0 20. lim (x + 9) = 9 x→0arrow_forward
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