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50 Define f(x) = sin x +} sin 3x + † sin 5x + …* (n terms). Graph fs and f1o from -n to n. Zoom in and describe the Gibbs phenomenon at x= 0.

50 Define f(x) = sin x +} sin 3x + † sin 5x + …* (n terms). Graph fs and f1o from -n to n. Zoom in and describe the Gibbs phenomenon at x= 0.

Advanced Engineering Mathematics
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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Please graph using a online program like desmos

**Problem 50**: Define \( f_n(x) = \sin x + \frac{1}{3} \sin 3x + \frac{1}{5} \sin 5x + \cdots \) (n terms). Graph \( f_5 \) and \( f_{10} \) from \(-\pi\) to \(\pi\). Zoom in and describe the Gibbs phenomenon at \( x = 0 \).
Transcribed Image Text:**Problem 50**: Define \( f_n(x) = \sin x + \frac{1}{3} \sin 3x + \frac{1}{5} \sin 5x + \cdots \) (n terms). Graph \( f_5 \) and \( f_{10} \) from \(-\pi\) to \(\pi\). Zoom in and describe the Gibbs phenomenon at \( x = 0 \).
Expert Solution
Step 1

given , 

fn(x) = sin x + 13sin 3x +15sin 5x +17sin 7x . . . . .   ( up-to n-terms )

we have , to find graph of f5 and f10 from  -π toπ .

and have to describe Gibbs phenomenon at x=0 .

 

The Gibbs phenomenon is a specific behavior of some functions manifested as over- and undershoots around a jump discontinuity .

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