Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)
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 12E
To determine

To evaluate: The value of limθ0θ+sinθtanθ using L’Hôpital’s Rule if appropriate.

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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 -00
Find the limits in Exercises 33–35  Are the functions continuous at the point being approached?
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→0
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