First slide

Functions (XII)

Question

If the period of the function $f (x) = \sin (\sqrt{[n]} x),$ where [n] denotes the greatest integer less than or equal to n, is 2 $π$ , then

Moderate

A

1 ≤ n < 2
B

1 < n < 2
C

1 ≤ n ≤ 2
D

None of these

Solution

Sin x is a periodic function with period 2 $π$ , therefore $\sin (\sqrt{[n]} x)$ is a periodic function with period $\frac{2 π}{\sqrt{[n]}}$ .
But the period of f (x) is 2 $π$ (given).
$∴ \frac{2 π}{\sqrt{[n]}} = 2 π \Rightarrow \sqrt{[n]} = 1 \Rightarrow [n] = 1 \Rightarrow 1 \leq n < 2$

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