#### Explain solution RD Sharma class 12 chapter 8 Continuity exercise multiple choice question 24 maths

The correct option is (C)

Hint:

If a function f  is continuous at x = a, then

$\lim _{x \rightarrow a-} f(x)=\lim _{x \rightarrow a^{+}} f(x)=f(a)$

Given:

the function

$f(x)= tan\: x$

Solution:

Step 1: Check continuity of the function

$f(x)=\tan x \text { on the set }\{n \pi: n \in Z\}$

$\therefore f(x)=\tan n \pi$

is defined at the integral point

Check continuity of the function

$f(x)=\tan x \text { on the set }\{2 n \pi: n \in Z\}$

$f(x)=\tan 2 n \pi$

is defined at the integral point

Check continuity of the function

$f(x)=\tan x \text { on the set }\left\{(2 n+1) \frac{\pi}{2}: n \in Z\right\}$

$f(x)=\tan (2 n+1) \frac{\pi}{2}$

is defined at the integral point

\begin{aligned} &f(x)=\tan \left(n \pi+\frac{\pi}{2}\right) \\ &f(x)=-\cot (n \pi) \end{aligned}

is not defined at the integral point

Check continuity of the function

$f(x)=\tan x \text { on the set }\left\{\frac{n \pi}{2}: n \in Z\right\}$

$f(x)=\tan \frac{n \pi}{2}$

is defined at the integral point

Hence, the correct answer is option (c)