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
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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
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 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_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_forwardFor the function f graphed as follows, approximate each of the limits and values in Exercises 31–34: 3 1. + + -4 -3 -2/-1 1 2 4 -2- 31. lim f(x), lim f(x), lim_f(x), and f(-2). X-2- X-2+" X-2 32. lim f(x), lim f(x), lim f(x), and f(-1). x-1-* X-1+ X-1 33. lim f(x), lim f(x), lim f(x), and f(2). X2- x+2+ X+2 34. lim f(x), lim f(x), lim f(x), and lim f(x). x-00 3.arrow_forward
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- Describe the Limit Laws?arrow_forwardDAPAWAN Apply lim sin a = 1 to obtain the limit of the following: I. a-0 a sin5x 1. lim 2. lim 0 csc 20 tan?x MOCAT USM 1983 199s 3. lim sin2ß B-0 sin3ß 4. lim x2 5. lim X-0 tanx KIDAPAWAN CITY C tan3x 6. lim X-0 tan4x 7. lim xcsc2x DAPAWAN 8. lim xcot3x X-n 9. lim xn sin x Hint: let a = x – 1, then lim a-0 sin(a+n) 2y+n 10. lim y-- cos 0arrow_forwardb) lim(1+ tan 3x)arrow_forward
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