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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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
Transcribed Image Text: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?
Transcribed Image Text: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×n+x)=g(x)

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