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sin(4z) f(x) = 9x 0.4 0.35 0.3 0.25 0/5 -0.25 0.25 sin(4x) Evaluate lim 9x Enter at least 3 decimal places in your answer

sin(4z) f(x) = 9x 0.4 0.35 0.3 0.25 0/5 -0.25 0.25 sin(4x) Evaluate lim 9x Enter at least 3 decimal places in your answer

Calculus: Early Transcendentals
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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The image shows a graph representing the function \( f(x) = \frac{\sin(4x)}{9x} \). The graph appears as a smooth curve, symmetrical about the y-axis, with the following features: - The graph is plotted on a coordinate plane with x-values ranging approximately from \(-0.5\) to \(0.5\). - The y-axis values labeled on the graph increase in increments of approximately 0.05, ranging from 0 to 0.4. - The curve has a peak value at the origin and tapers off towards the horizontal axis symmetrically on both sides. Task: Evaluate \(\lim_{{x \to 0}} \frac{\sin(4x)}{9x}\) and enter your answer with at least three decimal places. This graph visually represents the behavior of the given function as x approaches 0, illustrating the concept of a limit for an educational context.
Transcribed Image Text:The image shows a graph representing the function \( f(x) = \frac{\sin(4x)}{9x} \). The graph appears as a smooth curve, symmetrical about the y-axis, with the following features: - The graph is plotted on a coordinate plane with x-values ranging approximately from \(-0.5\) to \(0.5\). - The y-axis values labeled on the graph increase in increments of approximately 0.05, ranging from 0 to 0.4. - The curve has a peak value at the origin and tapers off towards the horizontal axis symmetrically on both sides. Task: Evaluate \(\lim_{{x \to 0}} \frac{\sin(4x)}{9x}\) and enter your answer with at least three decimal places. This graph visually represents the behavior of the given function as x approaches 0, illustrating the concept of a limit for an educational context.
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