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 14E
To determine
To evaluate: The value of
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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
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
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.)
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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- 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→0arrow_forwardFind the limits in Exercises 9–12. sin 2x cos 0 9. lim 10. lim 0→- 30 х r + sin r 2r + 7 – 5 sin r 2 – t + sin t 11. lim 12. lim t + cos t r 00arrow_forwardIn Exercises 7–10, use the formal definition of limit to prove that the function is continuous at c.arrow_forward
- In Exercises 49–54, show that the limits do not exist. xy? ху + 1 49. (х, у) —(1,1) у — 1 50. (x, y)→(1, –1) x² – y? lim lim lim x In y хе 52. (х, у) —-(1,0) хе —1 + у 51. lim (x, y)→(0,1) x² + (In y)² tan y – y tan x у — х y + sin x 53. (x, y)→(0,0) X + sin y 54. lim (х, у) ——(1,1) limarrow_forwardFind the limits in Exercises 49–56. lim V1 + cos ( csc x) 49. lim sin x-2 50. х x→-7/6 sin 0 tan 0 – 1 51. lim 52. lim п 53. lim sec e* + ™ tan 4 sec x T + tan x 54. lim sin x→0 tan x – 2 sec x sin t по 55. lim tan( 1 56. lim cos sin 0 t→0 0→0arrow_forwardFind the limits in Exercises 13–2 . by rewriting the fractions first. 13. lim (х, у) — (1,1) x² – 2xy + y² х — у x? - y? х — у 14. lim (х, у) —— (1,1) x+y x+y ху — у — 2х + 2 15. lim (х, у) ——(1,1) x#1 х — 1 y + 4 16. lim (х, у) —-(2, —4) х2у — ху + 4х2 — 4х x#-4, x#x² * - y + 2Vx – 2vy Vx - Vy 17. lim (х, у) —— (0,0) x*yarrow_forward
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