dx Jo (1 + x)Vz

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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+ lim f(x) dx + 0 Jeth
9.2
40%
5:34
K/s
Exam on impr..
Quiz on Improper Integrals
dx
dx
x2 - 2x
3
Jo (1 + x)V
Find the area bounded by the curve y = 1/Vx(2 – x), its asymptotes,
and the x axis.
Find the area between the curve y = 1/(ez + e-2) and the x axis.
Find the area between the witch y = 8a°/(x2 + 4a2) and its asymptote.
%3D
Find the volume generated if the first-quadrant area under the curve
y = e-z is revolved about the x axis.
Find the volume generated if the area under the curve y = Vze-z* is
revolved about the x axis.
Determine whether the following integrals converge or diverge.
dx
J. Vx + **
dx
Hint: Compare with J.
o dx
Hint: Compare with .
dx
Vx + x4
dx
Jo V2x – x²
Hint: Observe that 2 – x > x, for 0 < x < 1.
If h > 0 and the function f(x) is continuous for all x in the domain
a s *s b except x = c, where a < c < b, give an example to show
that
rc-h
lim J." s() dx + J s4) dx| + lim "/(*) dx + lim , f4) dx.
(x) dx.
a
Joth
h→0 Ja
If h > 0 and the function f(x) is continuous for all real values of x,
give an example to show that
L(4) dx # lim f(») dx + lim f(2) dx.
lim
f(x)
ho Ja
Transcribed Image Text:+ lim f(x) dx + 0 Jeth 9.2 40% 5:34 K/s Exam on impr.. Quiz on Improper Integrals dx dx x2 - 2x 3 Jo (1 + x)V Find the area bounded by the curve y = 1/Vx(2 – x), its asymptotes, and the x axis. Find the area between the curve y = 1/(ez + e-2) and the x axis. Find the area between the witch y = 8a°/(x2 + 4a2) and its asymptote. %3D Find the volume generated if the first-quadrant area under the curve y = e-z is revolved about the x axis. Find the volume generated if the area under the curve y = Vze-z* is revolved about the x axis. Determine whether the following integrals converge or diverge. dx J. Vx + ** dx Hint: Compare with J. o dx Hint: Compare with . dx Vx + x4 dx Jo V2x – x² Hint: Observe that 2 – x > x, for 0 < x < 1. If h > 0 and the function f(x) is continuous for all x in the domain a s *s b except x = c, where a < c < b, give an example to show that rc-h lim J." s() dx + J s4) dx| + lim "/(*) dx + lim , f4) dx. (x) dx. a Joth h→0 Ja If h > 0 and the function f(x) is continuous for all real values of x, give an example to show that L(4) dx # lim f(») dx + lim f(2) dx. lim f(x) ho Ja
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