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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Question
Determine if the given is divergent or convergent using the theorem.
![MUST REMEMBER! For integrals of functions with infinite discontinuity over bounded
intervals:
Theorem 3.11. Assume that f is continuous on the indicated interval.
1. On (a, b], with lim f(x) = ±0, we have
f(x) dx = lim| f(x) dx .
t-a
2. On [a, b), with lim f(x) = ±∞, we have
f(x) dx = lim
s-b
f(x) dx .
3. On [a, b], except at ce (a, b) with lim|f(x)| = +∞, we have
f(x
f(x)
= lim f(x) dx + lim f(x) dx.
provided these limits exist (i.e. finite number). The improper integral is said to be convergent if the
corresponding limit exists. Else, it is divergent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41e6e0d4-107f-4584-8223-4767d26289c1%2F0731c36c-1347-49f2-b52e-0ee023e7388e%2Fktgt8b_processed.png&w=3840&q=75)
Transcribed Image Text:MUST REMEMBER! For integrals of functions with infinite discontinuity over bounded
intervals:
Theorem 3.11. Assume that f is continuous on the indicated interval.
1. On (a, b], with lim f(x) = ±0, we have
f(x) dx = lim| f(x) dx .
t-a
2. On [a, b), with lim f(x) = ±∞, we have
f(x) dx = lim
s-b
f(x) dx .
3. On [a, b], except at ce (a, b) with lim|f(x)| = +∞, we have
f(x
f(x)
= lim f(x) dx + lim f(x) dx.
provided these limits exist (i.e. finite number). The improper integral is said to be convergent if the
corresponding limit exists. Else, it is divergent.
Transcribed Image Text:1
dx
(х + 1)2
-2
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