To determine The fundamental periods of the functions cos n x , sin n x , cos 2 π x k , sin 2 π x k , cos 2 π n x k and sin 2 π n x k . Explanation Result used: The fundamental period is the smallest positive period. That is, the smallest p such that f ( x + p ) = f ( x ) . The period of the functions of the form f ( x ) = a cos ( b x ± c ) ± d or f ( x ) = a sin ( b x ± c ) ± d is 2 π | b | . Calculation: Calculate the period of cos n x and sin n x as shown below. p = 2 π n That is, the period is 2 π n . Similarly, obtain the period of cos 2 π x k and sin 2 π x k as follows. p = 2 π 2 π k = k That is, the period of cos 2 π x k and sin 2 π x k is k

10th Edition

ISBN: 9781119096023

Author: Kreyszig

Publisher: WILEY

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Chapter 11.1, Problem 2P

To determine

The fundamental periods of the functions cosnx,sinnx,cos2πxk,sin2πxk,cos2πnxk and sin2πnxk.

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Chapter 11.1, Problem 1P

Chapter 11.1, Problem 3P

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Ch. 11.1 - Prob. 1P Ch. 11.1 - PERIOD, FUNDAMENTAL PERIOD The fundamental period...Ch. 11.1 - PERIOD, FUNDAMENTAL PERIOD The fundamental period...Ch. 11.1 - PERIOD, FUNDAMENTAL PERIOD The fundamental period...Ch. 11.1 - PERIOD, FUNDAMENTAL PERIOD The fundamental period...Ch. 11.1 - GRAPHS OF 2π–PERIODIC FUNCTIONS Sketch or graph...Ch. 11.1 - GRAPHS OF 2π–PERIODIC FUNCTIONS Sketch or graph...Ch. 11.1 - GRAPHS OF 2π–PERIODIC FUNCTIONS Sketch or graph...Ch. 11.1 - GRAPHS OF 2π–PERIODIC FUNCTIONS Sketch or graph...Ch. 11.1 - GRAPHS OF 2π–PERIODIC FUNCTIONS Sketch or graph...

Ch. 11.1 - Prob. 11P Ch. 11.1 - FOURIER SERIES Find the Fourier series of the...Ch. 11.1 - FOURIER SERIES Find the Fourier series of the...Ch. 11.1 - FOURIER SERIES Find the Fourier series of the...Ch. 11.1 - FOURIER SERIES Find the Fourier series of the...Ch. 11.1 - FOURIER SERIES Find the Fourier series of the...Ch. 11.1 - FOURIER SERIES Find the Fourier series of the...Ch. 11.1 - FOURIER SERIES Find the Fourier series of the...Ch. 11.1 - FOURIER SERIES Find the Fourier series of the...Ch. 11.1 - FOURIER SERIES Find the Fourier series of the...Ch. 11.1 - FOURIER SERIES Find the Fourier series of the...Ch. 11.1 - Prob. 23P Ch. 11.2 - EVEN AND ODD FUNCTIONS Are the following functions...Ch. 11.2 - EVEN AND ODD FUNCTIONS Are the following functions...Ch. 11.2 - EVEN AND ODD FUNCTIONS Are the following functions...Ch. 11.2 - Prob. 4P Ch. 11.2 - EVEN AND ODD FUNCTIONS Are the following functions...Ch. 11.2 - Prob. 6P Ch. 11.2 - EVEN AND ODD FUNCTIONS Are the following functions...Ch. 11.2 - Prob. 8P Ch. 11.2 - Prob. 9P Ch. 11.2 - Prob. 10P Ch. 11.2 - Prob. 11P Ch. 11.2 - Prob. 12P Ch. 11.2 - Prob. 13P Ch. 11.2 - Prob. 14P Ch. 11.2 - Prob. 15P Ch. 11.2 - Prob. 16P Ch. 11.2 - Prob. 17P Ch. 11.2 - Prob. 18P Ch. 11.2 - Prob. 19P Ch. 11.2 - Prob. 20P Ch. 11.2 - Prob. 22P Ch. 11.2 - Prob. 23P Ch. 11.2 - Prob. 24P Ch. 11.2 - Prob. 25P Ch. 11.2 - Prob. 26P Ch. 11.2 - Prob. 27P Ch. 11.2 - Prob. 28P Ch. 11.2 - Prob. 29P Ch. 11.2 - Prob. 30P Ch. 11.3 - Prob. 1P Ch. 11.3 - Prob. 2P Ch. 11.3 - Prob. 3P Ch. 11.3 - Prob. 4P Ch. 11.3 - Prob. 5P Ch. 11.3 - Prob. 6P Ch. 11.3 - Prob. 7P Ch. 11.3 - Prob. 8P Ch. 11.3 - Prob. 9P Ch. 11.3 - Prob. 10P Ch. 11.3 - Prob. 11P Ch. 11.3 - Prob. 13P Ch. 11.3 - Prob. 14P Ch. 11.3 - Prob. 15P Ch. 11.3 - Prob. 16P Ch. 11.3 - Prob. 17P Ch. 11.3 - Prob. 18P Ch. 11.3 - Prob. 19P Ch. 11.4 - Prob. 2P Ch. 11.4 - Prob. 3P Ch. 11.4 - Prob. 4P Ch. 11.4 - Prob. 5P Ch. 11.4 - Prob. 6P Ch. 11.4 - Prob. 7P Ch. 11.4 - Prob. 8P Ch. 11.4 - Prob. 9P Ch. 11.4 - Prob. 11P Ch. 11.4 - Prob. 12P Ch. 11.4 - Prob. 13P Ch. 11.4 - Prob. 14P Ch. 11.4 - Prob. 15P Ch. 11.5 - Prob. 1P Ch. 11.5 - Prob. 2P Ch. 11.5 - Prob. 3P Ch. 11.5 - Prob. 4P Ch. 11.5 - Prob. 5P Ch. 11.5 - Prob. 6P Ch. 11.5 - Prob. 7P Ch. 11.5 - Prob. 8P Ch. 11.5 - Prob. 9P Ch. 11.5 - Prob. 10P Ch. 11.5 - Prob. 11P Ch. 11.5 - Prob. 12P Ch. 11.5 - Prob. 13P Ch. 11.6 - Prob. 1P Ch. 11.6 - Prob. 2P Ch. 11.6 - Prob. 3P Ch. 11.6 - Prob. 4P Ch. 11.6 - Prob. 5P Ch. 11.6 - Prob. 6P Ch. 11.6 - Prob. 7P Ch. 11.7 - Prob. 1P Ch. 11.7 - Prob. 2P Ch. 11.7 - Prob. 3P Ch. 11.7 - Prob. 4P Ch. 11.7 - Prob. 5P Ch. 11.7 - Prob. 6P Ch. 11.7 - Prob. 7P Ch. 11.7 - Prob. 8P Ch. 11.7 - Prob. 9P Ch. 11.7 - Prob. 10P Ch. 11.7 - Prob. 11P Ch. 11.7 - Prob. 12P Ch. 11.7 - Prob. 16P Ch. 11.7 - Prob. 17P Ch. 11.7 - Prob. 18P Ch. 11.7 - Prob. 19P Ch. 11.7 - Prob. 20P Ch. 11.8 - Prob. 1P Ch. 11.8 - Prob. 2P Ch. 11.8 - Prob. 3P Ch. 11.8 - Prob. 4P Ch. 11.8 - Prob. 5P Ch. 11.8 - Prob. 6P Ch. 11.8 - Prob. 7P Ch. 11.8 - Prob. 8P Ch. 11.8 - Prob. 9P Ch. 11.8 - Prob. 10P Ch. 11.8 - Prob. 11P Ch. 11.8 - Prob. 12P Ch. 11.8 - Prob. 13P Ch. 11.8 - Prob. 14P Ch. 11.9 - Prob. 1P Ch. 11.9 - Prob. 2P Ch. 11.9 - Prob. 3P Ch. 11.9 - Prob. 4P Ch. 11.9 - Prob. 5P Ch. 11.9 - Prob. 6P Ch. 11.9 - Prob. 7P Ch. 11.9 - Prob. 8P Ch. 11.9 - Prob. 9P Ch. 11.9 - Prob. 10P Ch. 11.9 - Prob. 11P Ch. 11.9 - Prob. 12P Ch. 11.9 - Prob. 13P Ch. 11.9 - Prob. 14P Ch. 11.9 - Prob. 15P Ch. 11.9 - Prob. 17P Ch. 11.9 - Prob. 18P Ch. 11.9 - Prob. 19P Ch. 11.9 - Prob. 20P Ch. 11.9 - Prob. 21P Ch. 11.9 - Prob. 22P Ch. 11.9 - Prob. 23P Ch. 11.9 - Prob. 24P Ch. 11 - Prob. 1RQ Ch. 11 - Prob. 2RQ Ch. 11 - Prob. 3RQ Ch. 11 - Prob. 4RQ Ch. 11 - Prob. 5RQ Ch. 11 - Prob. 6RQ Ch. 11 - Prob. 7RQ Ch. 11 - Prob. 8RQ Ch. 11 - Prob. 9RQ Ch. 11 - Prob. 10RQ Ch. 11 - Prob. 11RQ Ch. 11 - Prob. 12RQ Ch. 11 - Prob. 13RQ Ch. 11 - Prob. 14RQ Ch. 11 - Prob. 15RQ Ch. 11 - Prob. 16RQ Ch. 11 - Prob. 17RQ Ch. 11 - Prob. 18RQ Ch. 11 - Prob. 19RQ Ch. 11 - Prob. 20RQ Ch. 11 - Prob. 21RQ Ch. 11 - Prob. 22RQ Ch. 11 - Prob. 23RQ Ch. 11 - Prob. 24RQ Ch. 11 - Prob. 25RQ Ch. 11 - Prob. 26RQ Ch. 11 - Prob. 27RQ Ch. 11 - Prob. 28RQ Ch. 11 - Prob. 29RQ Ch. 11 - Prob. 30RQ

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