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 9E
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
Find the limits in Exercises 33–35 Are the functions continuous at the point being approached?
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 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 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_forwardIn Exercises 7–10, use the formal definition of limit to prove that the function is continuous at c.arrow_forward
- Evaluate the limit lim (sin(4x + 5) + 5) = I+ 00arrow_forwardUnit 3: Curve Sketching 12. When does a limit not exist?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_forward
- Use 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_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_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_forward
- 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)arrow_forwardFind the limit analyticallyarrow_forwardDescribe the Limit Laws?arrow_forward
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Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY