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

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

Answers (1)

Answer:

 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)

Posted by

Gurleen Kaur

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