CALCULUS: EARLY TRANSCENDENTALS
9th Edition
ISBN: 9780357375808
Author: Stewart
Publisher: CENGAGE L
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Chapter B, Problem 11E
To determine
Show that the triangle with vertices
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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 B Solutions
CALCULUS: EARLY TRANSCENDENTALS
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. 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. 34ECh. B - Prob. 35ECh. B - Prob. 36ECh. B - Prob. 37ECh. B - Prob. 38ECh. B - Prob. 39ECh. B - Prob. 40ECh. B - Prob. 41ECh. B - Prob. 42ECh. B - Prob. 43ECh. B - Prob. 44ECh. B - Prob. 45ECh. B - Prob. 46ECh. B - Prob. 47ECh. B - Prob. 48ECh. B - Prob. 49ECh. B - Prob. 50ECh. B - Prob. 51ECh. B - Prob. 52ECh. B - Prob. 53ECh. B - Prob. 54ECh. B - Prob. 55ECh. B - Prob. 56ECh. B - Prob. 57ECh. B - Prob. 58ECh. B - Prob. 59ECh. B - Prob. 60ECh. B - Prob. 61E
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