Determine if the given is divergent or convergent using the theorem. MUST REMEMBER! For integrals of functions with infinite discontinuity over boundedintervals:Theorem 3.11. Assume that f is continuous on the indicated interval.1. On (a, b], with lim f(x) = ±0, we havef(x) dx = lim| f(x) dx .t-a2. On [a, b), with lim f(x) = ±∞, we havef(x) dx = lims-bf(x) dx .3. On [a, b], except at ce (a, b) with lim|f(x)| = +∞, we havef(xf(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 thecorresponding limit exists. Else, it is divergent. 1dx(х + 1)2-2

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1 (x + 1)2 dx -2

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.

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