10. Suppose is a periodic function with period 11. What is the smallest period possible for the multivariate function and in what direction does it occur? Suppose g(x) is a periodic function with period 11. What is the smallest period possible for the multivariate function g(3x + 7y) and in what direction does it occur?

Answered: Suppose is a periodic function with…

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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10. Suppose is a periodic function with period 11. What is the smallest period possible for the multivariate function and in what direction does it occur?

Suppose g(x) is a periodic function with period 11. What is the smallest period possible for the

multivariate function g(3x + 7y) and in what direction does it occur?

Expert Solution

Step 1

The smallest period (if exists) of function is the smallest positive number T that satisfies the equality $f (x + T) = f (x) .$ Occasionally, the smallest period is called 'the period' or the 'prime period' of the function.

One of the properties of a periodic function is that it's values repeat after every period, both in the positive and negative directions on the number line.

Since the value of $X$ is $11$ the values of the function $g (x)$ repeats after $X = 11$

Or in algebraic notation it can be written as:

$g (11 \times n + x) = g (x)$