First slide

Functions (XII)

Question

The period of the function $f (x) = \cos (\frac{πx}{n!}) - \sin (\frac{πx}{(n + 1)!}) is$

Moderate

A

2 (n + 1)!
B

2 (n!)
C

(n + 1)
D

Not periodic

Solution

Since sin x and cos x are periodic functions with period 2 $π$ .
$∴ Period of \cos (\frac{πx}{n!}) = \frac{2 π}{π / n!} = 2 (n!) and period of \sin (\frac{πx}{(n + 1)!}) = \frac{2 π}{π / (n + 1)!} = 2 (n + 1)!$
$∴$ Period of f (x) = L.C.M. of {2 (n!), 2 (n + 1)!} = 2 (n + 1)!

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App