Which of the following function is periodic with period π ?

Question

Which of the following function is periodic with period π ? (A)  f(x)=x cos x  (B)  f(x)=| cos x|  (C)  f(x)= sin x  (D)  f(x)=[x+π ] Where [x] means the greater integer not greater than x.

Tardigrade Admin · Accepted Answer

(a) f(x)=x cos x It is not periodic for any period (b) f(x)= | cos x| It is periodic for the period π (c) f(x)= sin x It is periodic for the period 2 π (d) f(x)=[x+π ] It is not periodic with period π ∴ Option (b) is correct.

Q. Which of the following function is periodic with period $π$ ?

$f (x) = x cos x$

$f (x) = ∣ cos x ∣$

$f (x) = sin x$

$f (x) = [x + π]$ Where $[x]$ means the greater integer not greater than $x .$

(a) $f (x) = x cos x$ It is not periodic for any period
(b) $f (x) = ∣ cos x ∣$ It is periodic for the period $π$
(c) $f (x) = sin x$ It is periodic for the period $2 π$
(d) $f (x) = [x + π]$ It is not periodic with period $π$
$∴$ Option (b) is correct.

Q. Which of the following function is periodic with period π ?

f(x)=xcosx

f(x)=∣cosx∣

f(x)=sinx

f(x)=[x+π] Where [x] means the greater integer not greater than x.