Precalculus: A Unit Circle Approach (3rd Edition)
3rd Edition
ISBN: 9780134433042
Author: J. S. Ratti, Marcus S. McWaters, Leslaw Skrzypek
Publisher: PEARSON
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Chapter A.1, Problem 45E
To determine
To use the absolute value to express the distance between the points with coordinates a and b on the number line. Then to determine the distance by evaluating the absolute value 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
1. Compute
Lo
F⚫dr, where
and C is defined by
F(x, y) = (x² + y)i + (y − x)j
r(t) = (12t)i + (1 − 4t + 4t²)j
from the point (1, 1) to the origin.
Chapter A.1 Solutions
Precalculus: A Unit Circle Approach (3rd Edition)
Ch. A.1 - In Exercises 1-4, write each of the following...Ch. A.1 - In Exercises 1-4, write each of the following...Ch. A.1 - In Exercises 1-4, write each of the following...Ch. A.1 - Prob. 4ECh. A.1 - Prob. 5ECh. A.1 - Prob. 6ECh. A.1 - Prob. 7ECh. A.1 - Prob. 8ECh. A.1 - In Exercises 5-10, classify each of the following...Ch. A.1 - Prob. 10E
Ch. A.1 - Prob. 11ECh. A.1 - Prob. 12ECh. A.1 - Prob. 13ECh. A.1 - Prob. 14ECh. A.1 - Prob. 15ECh. A.1 - Prob. 16ECh. A.1 - Prob. 17ECh. A.1 - Prob. 18ECh. A.1 - Prob. 19ECh. A.1 - Prob. 20ECh. A.1 - Prob. 21ECh. A.1 - Prob. 22ECh. A.1 - Prob. 23ECh. A.1 - Prob. 24ECh. A.1 -
In Exercises 25-38, rewrite each expression...Ch. A.1 - Prob. 26ECh. A.1 - Prob. 27ECh. A.1 - Prob. 28ECh. A.1 - Prob. 29ECh. A.1 - Prob. 30ECh. A.1 - Prob. 31ECh. A.1 - Prob. 32ECh. A.1 - Prob. 33ECh. A.1 - Prob. 34ECh. A.1 - Prob. 35ECh. A.1 - Prob. 36ECh. A.1 - Prob. 37ECh. A.1 - Prob. 38ECh. A.1 - Prob. 39ECh. A.1 - Prob. 40ECh. A.1 - Prob. 41ECh. A.1 - Prob. 42ECh. A.1 - Prob. 43ECh. A.1 - Prob. 44ECh. A.1 - Prob. 45ECh. A.1 - Prob. 46ECh. A.1 - Prob. 47ECh. A.1 - Prob. 48ECh. A.1 - Prob. 49ECh. A.1 - Prob. 50ECh. A.1 - Prob. 51ECh. A.1 - Prob. 52ECh. A.1 - Prob. 53ECh. A.1 - Prob. 54ECh. A.1 - Prob. 55ECh. A.1 - Prob. 56ECh. A.1 - Prob. 57ECh. A.1 - Prob. 58ECh. A.1 - Prob. 59ECh. A.1 - Prob. 60ECh. A.1 - Prob. 61ECh. A.1 - Prob. 62ECh. A.1 - Prob. 63ECh. A.1 - Prob. 64ECh. A.1 - Prob. 65ECh. A.1 - Prob. 66ECh. A.1 - Prob. 67ECh. A.1 -
In Exercises 59-68, evaluate each expression for...Ch. A.1 - Prob. 69ECh. A.1 - Prob. 70ECh. A.1 - Prob. 71ECh. A.1 - Prob. 72ECh. A.1 - Prob. 73ECh. A.1 - Prob. 74ECh. A.1 - Prob. 75ECh. A.1 - Prob. 76ECh. A.1 - Prob. 77ECh. A.1 - Prob. 78ECh. A.1 - Prob. 79ECh. A.1 - Prob. 80ECh. A.1 - Prob. 81ECh. A.1 - Prob. 82ECh. A.1 - Prob. 83ECh. A.1 - Prob. 84ECh. A.1 - Prob. 85ECh. A.1 - Prob. 86ECh. A.1 - Prob. 87ECh. A.1 - Prob. 88ECh. A.1 - Prob. 89ECh. A.1 - Prob. 90ECh. A.1 - Prob. 91ECh. A.1 - Prob. 92ECh. A.1 - Prob. 93ECh. A.1 - Prob. 94ECh. A.1 - Prob. 95ECh. A.1 - Prob. 96ECh. A.1 - Prob. 97ECh. A.1 - Prob. 98ECh. A.1 - Prob. 99ECh. A.1 - Prob. 100ECh. A.1 - Prob. 101ECh. A.1 - Prob. 102ECh. A.1 - Prob. 103ECh. A.1 - Prob. 104ECh. A.1 - Prob. 105ECh. A.1 - Prob. 106ECh. A.1 - Prob. 107ECh. A.1 - Prob. 108ECh. A.1 - Prob. 109ECh. A.1 - In Exercises 101-134, simplify each expression....Ch. A.1 - Prob. 111ECh. A.1 - Prob. 112ECh. A.1 - Prob. 113ECh. A.1 - Prob. 114ECh. A.1 - Prob. 115ECh. A.1 - Prob. 116ECh. A.1 - Prob. 117ECh. A.1 - Prob. 118ECh. A.1 - Prob. 119ECh. A.1 - Prob. 120ECh. A.1 - Prob. 121ECh. A.1 - Prob. 122ECh. A.1 - Prob. 123ECh. A.1 - Prob. 124ECh. A.1 - Prob. 125ECh. A.1 - Prob. 126ECh. A.1 - Prob. 127ECh. A.1 - Prob. 128ECh. A.1 - Prob. 129ECh. A.1 - Prob. 130ECh. A.1 - Prob. 131ECh. A.1 - Prob. 132ECh. A.1 - Prob. 133ECh. A.1 - Prob. 134ECh. A.1 - Prob. 135ECh. A.1 - Prob. 136ECh. A.1 - Prob. 137ECh. A.1 - Prob. 138ECh. A.1 - Prob. 139ECh. A.1 - Prob. 140ECh. A.1 - Prob. 141ECh. A.1 - Prob. 142E
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