Question

Show that the following functions are non periodic
1.x+sinx
2.cosx+(x) where (x) is fractional part of x.

Answer 1

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MATHS

Asked on December 30, 2019 byQuadri Sayyed

Consider the function f(x)=sin(kx)+{x}, where {x} represents the fractional part function

Statement 1: f(x) is periodic for k=mπ, where m is a rational number

Statement 2: The sum of two periodic functions is always periodic

A

If both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1

B

If both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE

D

If STATEMENT 1 is FALSE and STATEMENT 2 is TRUE

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ANSWER

Period of sin(kx) is k2π

period of x is 1

Hence period of f(x) is LCM of k2π and 1.

since 1 is a rational number hence k2π should be rational number to get the LCM

Hence k=mπ where m is a rational number.

Sum of two periodic function is periodic if both the function has either rational period or irrational period of same category.

Step-by-step explanation:

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