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
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
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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![1. Consider the improper integral
\[
\int_{0}^{\infty} \frac{e^x}{e^{2x} + 3} \, dx
\]
a) [Instructions Redacted] Determine whether the integral above converges or diverges. If it converges, determine the value of the integral.
b) [Instructions Redacted] Explain why the inequality below is true for \( x \geq 0 \).
\[
\frac{e^x (\sin^2 x)}{e^{2x} + 3 + x^2} \leq \frac{e^x}{e^{2x} + 3}
\]
c) [Instructions Redacted] Use the comparison test to determine whether the integral below converges or diverges.
\[
\int_{0}^{\infty} \frac{e^x (\sin^2 x)}{e^{2x} + 3 + x^2} \, dx
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F953e3ae3-1a36-4eca-a542-ddeb8c6ae72a%2F5cb15472-27dc-45d6-97d8-51419272702e%2Fn2nijc5_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider the improper integral
\[
\int_{0}^{\infty} \frac{e^x}{e^{2x} + 3} \, dx
\]
a) [Instructions Redacted] Determine whether the integral above converges or diverges. If it converges, determine the value of the integral.
b) [Instructions Redacted] Explain why the inequality below is true for \( x \geq 0 \).
\[
\frac{e^x (\sin^2 x)}{e^{2x} + 3 + x^2} \leq \frac{e^x}{e^{2x} + 3}
\]
c) [Instructions Redacted] Use the comparison test to determine whether the integral below converges or diverges.
\[
\int_{0}^{\infty} \frac{e^x (\sin^2 x)}{e^{2x} + 3 + x^2} \, dx
\]
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