sin 2x lim

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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Find the limit

The image shows a mathematical limit expression, which can be transcribed as:

37. \(\lim_{{x \to \infty}} \frac{{\sin 2x}}{x}\)

This limit evaluates the behavior of the function \(\frac{\sin 2x}{x}\) as \(x\) approaches infinity. The sine function oscillates between -1 and 1, and as \(x\) becomes very large, the value of the fraction tends towards zero. This is because the sine function's oscillations become negligible in comparison to the growing magnitude of \(x\).
Transcribed Image Text:The image shows a mathematical limit expression, which can be transcribed as: 37. \(\lim_{{x \to \infty}} \frac{{\sin 2x}}{x}\) This limit evaluates the behavior of the function \(\frac{\sin 2x}{x}\) as \(x\) approaches infinity. The sine function oscillates between -1 and 1, and as \(x\) becomes very large, the value of the fraction tends towards zero. This is because the sine function's oscillations become negligible in comparison to the growing magnitude of \(x\).
Expert Solution
Step 1

Consider the given function,

limxsin2xx

since is a continuous periodic function, as sin2x-1,1.

as x approaches the infinity value of sin2x is lies between -1,1

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