APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI
10th Edition
ISBN: 9780357465400
Author: Tan
Publisher: CENGAGE L
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Chapter B, Problem 10E
To determine
To evaluate: The value of
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Students have asked these similar questions
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?
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
||
Chapter B Solutions
APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI
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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- 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_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
- 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 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_forwardEvaluate lim,0+ e(1/z) .arrow_forward
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