1. We know that lim as x approaches 0 (sin(x)/x) = 1 a) Explain why this limit statement implies the following approximation: (sin(x)/x) ≈ 1 if x ≈ 0. b) Rearranging this approximation, we get the smalll angle approximation: sin(x) ≈ x if x is small. Test this approximation with some small values of x )use radians). Share the result. Does this approxiamation work? c) Plot both y = sin(x) and y = x on the same axes, and show on the plot how and where the approximation is valid.
1. We know that lim as x approaches 0 (sin(x)/x) = 1 a) Explain why this limit statement implies the following approximation: (sin(x)/x) ≈ 1 if x ≈ 0. b) Rearranging this approximation, we get the smalll angle approximation: sin(x) ≈ x if x is small. Test this approximation with some small values of x )use radians). Share the result. Does this approxiamation work? c) Plot both y = sin(x) and y = x on the same axes, and show on the plot how and where the approximation is valid.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. We know that lim as x approaches 0 (sin(x)/x) = 1
a) Explain why this limit statement implies the following approximation:
(sin(x)/x) ≈ 1 if x ≈ 0.
b) Rearranging this approximation, we get the smalll angle approximation: sin(x) ≈ x if x is small. Test this approximation with some small values of x )use radians). Share the result. Does this approxiamation work?
c) Plot both y = sin(x) and y = x on the same axes, and show on the plot how and where the approximation is valid.
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