Developmental Mathematics (9th Edition)
9th Edition
ISBN: 9780321997173
Author: Marvin L. Bittinger, Judith A. Beecher
Publisher: PEARSON
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Chapter O, Problem 29ES
To determine
To calculate: The value of the expression
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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 O Solutions
Developmental Mathematics (9th Edition)
Ch. O - Prob. 1DECh. O - Prob. 2DECh. O - Prob. 3DECh. O - Prob. 4DECh. O - Prob. 5DECh. O - Prob. 6DECh. O - Prob. 7DECh. O - Prob. 8DECh. O - Prob. 9DECh. O - Prob. 10DE
Ch. O - Prob. 11DECh. O - Prob. 12DECh. O - Prob. 13DECh. O - Prob. 14DECh. O - Prob. 15DECh. O - Prob. 16DECh. O - Prob. 17DECh. O - Prob. 18DECh. O - Simplify.
19.
Ch. O - Prob. 20DECh. O - Prob. 21DECh. O - Prob. 22DECh. O - Prob. 23DECh. O - Prob. 24DECh. O - Prob. 25DECh. O - Find the conjugate.
26.
Ch. O - Prob. 27DECh. O - Prob. 28DECh. O - Prob. 29DECh. O - Prob. 30DECh. O - Prob. 31DECh. O - Prob. 32DECh. O - Prob. 33DECh. O - Prob. 34DECh. O - Prob. 36DECh. O - Prob. 37DECh. O - Prob. 38DECh. O - Prob. 1ESCh. O - Prob. 2ESCh. O - Prob. 3ESCh. O - Prob. 4ESCh. O - Prob. 5ESCh. O - Prob. 6ESCh. O - Prob. 7ESCh. O - Prob. 8ESCh. O - Prob. 9ESCh. O - Prob. 10ESCh. O - Prob. 11ESCh. O - Prob. 12ESCh. O - Prob. 13ESCh. O - Prob. 14ESCh. O - Prob. 15ESCh. O - Prob. 16ESCh. O - Prob. 17ESCh. O - Prob. 18ESCh. O - Prob. 19ESCh. O - Prob. 20ESCh. O - Prob. 21ESCh. O - Prob. 22ESCh. O - Prob. 23ESCh. O - Prob. 24ESCh. O - Prob. 25ESCh. O - Prob. 26ESCh. O - Prob. 27ESCh. O - Prob. 28ESCh. O - Prob. 29ESCh. O - Prob. 30ESCh. O - Prob. 31ESCh. O - Prob. 32ESCh. O - Prob. 33ESCh. O - Prob. 34ESCh. O - Prob. 35ESCh. O - Prob. 36ESCh. O - Prob. 37ESCh. O - Prob. 38ESCh. O - Prob. 39ESCh. O - Prob. 40ESCh. O - Prob. 41ESCh. O - Prob. 42ESCh. O - Prob. 43ESCh. O - Prob. 44ESCh. O - Prob. 45ESCh. O - Prob. 46ESCh. O - Prob. 47ESCh. O - Prob. 48ESCh. O - Prob. 50ESCh. O - Prob. 51ESCh. O - Prob. 52ESCh. O - Prob. 53ESCh. O - Prob. 54ESCh. O - Prob. 55ESCh. O - Prob. 56ESCh. O - Prob. 57ESCh. O - Prob. 58ESCh. O - Prob. 59ESCh. O - Prob. 60ESCh. O - Prob. 61ESCh. O - Prob. 62ESCh. O - Prob. 63ESCh. O - Prob. 64ESCh. O - Prob. 65ESCh. O - Prob. 66ESCh. O - Prob. 67ESCh. O - Prob. 68ESCh. O - Prob. 69ESCh. O - Prob. 70ESCh. O - Prob. 71ESCh. O - Prob. 72ESCh. O - Prob. 73ESCh. O - Prob. 74ESCh. O - Prob. 75ESCh. O - Prob. 76ESCh. O - Prob. 77ESCh. O - Prob. 78ESCh. O - Prob. 79ESCh. O - Prob. 80ESCh. O - Prob. 81ESCh. O - Prob. 82ESCh. O - Prob. 83ESCh. O - Prob. 84ESCh. O - Prob. 85ESCh. O - Prob. 86ESCh. O - Prob. 87ESCh. O - Prob. 88ESCh. O - Prob. 89ESCh. O - Prob. 90ESCh. O - Prob. 91ESCh. O - Prob. 92ESCh. O - Prob. 93ESCh. O - Prob. 94ESCh. O - Prob. 95ESCh. O - Prob. 96ESCh. O - Prob. 97ESCh. O - Prob. 98ESCh. O - Prob. 99ESCh. O - Prob. 100ESCh. O - Prob. 101ESCh. O - Prob. 102ESCh. O - Prob. 103ESCh. O - Prob. 104ESCh. O - Prob. 105ESCh. O - Prob. 106ESCh. O - Prob. 107ESCh. O - Prob. 108ESCh. O - Prob. 109ESCh. O - Prob. 110ESCh. O - Prob. 111ESCh. O - Prob. 112ESCh. O - Prob. 113ESCh. O - Prob. 114ES
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