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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Use the comparison Theorem to show that formula converges. (formula attached)
![The image shows the mathematical expression for an improper integral:
\[
\int_{1}^{\infty} \frac{\sin^2 x}{x^2} \, dx \text{ converges.}
\]
This indicates that the integral, which has limits from 1 to infinity, evaluates to a finite number, meaning it converges. The integrand is the function \(\frac{\sin^2 x}{x^2}\), where \(\sin^2 x\) is the square of the sine function, and \(x^2\) is \(x\) raised to the power of 2. The text states that this integral converges, suggesting that the area under the curve described by this function from \(x = 1\) to \(x = \infty\) is finite.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46320f22-15c6-4b1f-a7d5-cd512745aa96%2F9242b9b3-3d8e-4dcc-9c6e-4082765f47c5%2Ffevm98_processed.png&w=3840&q=75)
Transcribed Image Text:The image shows the mathematical expression for an improper integral:
\[
\int_{1}^{\infty} \frac{\sin^2 x}{x^2} \, dx \text{ converges.}
\]
This indicates that the integral, which has limits from 1 to infinity, evaluates to a finite number, meaning it converges. The integrand is the function \(\frac{\sin^2 x}{x^2}\), where \(\sin^2 x\) is the square of the sine function, and \(x^2\) is \(x\) raised to the power of 2. The text states that this integral converges, suggesting that the area under the curve described by this function from \(x = 1\) to \(x = \infty\) is finite.
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