Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
13th Edition
ISBN: 9780321869838
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
Publisher: PEARSON
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Textbook Question
Chapter A.4, Problem 5MP
Express as a simple fraction reduced to lowest terms:
(A)
(B)
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A function is defined on the interval (-π/2,π/2) by this multipart rule:
if -π/2 < x < 0
f(x) =
a
if x=0
31-tan x
+31-cot x
if 0 < x < π/2
Here, a and b are constants. Find a and b so that the function f(x) is continuous at x=0.
a=
b= 3
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
f(x) = (x + 4x4) 5,
a = -1
lim f(x)
X--1
=
lim
x+4x
X--1
lim
X-1
4
x+4x
5
))"
5
))
by the power law
by the sum law
lim (x) + lim
X--1
4
4x
X-1
-(0,00+(
Find f(-1).
f(-1)=243
lim (x) +
-1 +4
35
4 ([
)
lim (x4)
5
x-1
Thus, by the definition of continuity, f is continuous at a = -1.
by the multiple constant law
by the direct substitution property
Chapter A.4 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
Ch. A.4 - Reduce each fraction to lowest terms....Ch. A.4 - Reduce each rational expression to lowest terms....Ch. A.4 - Prob. 3MPCh. A.4 - Combine into a single fraction and reduce to...Ch. A.4 - Express as a simple fraction reduced to lowest...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 3ECh. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 5E
Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 7ECh. A.4 - Prob. 8ECh. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 14ECh. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 18ECh. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - Prob. 25ECh. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - Prob. 30ECh. A.4 - Prob. 31ECh. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - In Problems 2334, perform the indicated operations...Ch. A.4 - Prob. 34ECh. A.4 - Prob. 35ECh. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - Prob. 37ECh. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - In Problems 3542, imagine that the indicated...Ch. A.4 - Represent the compound fractions in Problems 4346...Ch. A.4 - Represent the compound fractions in Problems 4346...Ch. A.4 - Represent the compound fractions in Problems 4346...Ch. A.4 - Represent the compound fractions in Problems 4346...
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