ue of the integral. Explain why the inequality below is true for x > 0. ex e* (sin²x) e2x +3+x² ≤ e2x + 3 Use the comparison test to determine whether the integral below converges or diverges. 6. e² (sin² x) e2x +3+x² dx

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 5E: 5. Prove that the equation has no solution in an ordered integral domain.
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Question
1. Consider the improper integral
ex
1.
dx
e2x +3
a)
Determine whether the integral above converges or diverges. If it converges, determine
the value of the integral.
b)
Explain why the inequality below is true for x > 0.
e* (sin²x)
e²x +3+x²
<
ex
e2x + 3
Use the comparison test to determine whether the integral below converges or diverges.
So
e* (sin² x)
e²x +3+x²
dx
Transcribed Image Text:1. Consider the improper integral ex 1. dx e2x +3 a) Determine whether the integral above converges or diverges. If it converges, determine the value of the integral. b) Explain why the inequality below is true for x > 0. e* (sin²x) e²x +3+x² < ex e2x + 3 Use the comparison test to determine whether the integral below converges or diverges. So e* (sin² x) e²x +3+x² dx
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