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  • Please solve RD Sharma class 12 chapter 8 Continuity exercise multiple choice question 25 maths textbook solution

Please solve RD Sharma class 12 chapter 8 Continuity exercise multiple choice question 25 maths textbook solution

Answers (1)

Answer:

 The correct option is (b)

Hint:

 \lim _{x \rightarrow 0} \frac{\sin x}{x}=1

Given:

 f(x)= \begin{cases}\frac{\sin 3 x}{x} &, x \neq 0 \\ \frac{k}{2} &, x \neq 0\end{cases}

Solution:

is continuous at x = 0, then

LHL = RHL

\begin{aligned} &\lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0^{+}} f(x) \\ &\lim _{x \rightarrow 0^{-}} \frac{\sin 3 x}{x}=f(0) \end{aligned}

\begin{aligned} &\Rightarrow 3 \lim _{x \rightarrow 0} \frac{\sin 3 x}{3 x}=\frac{k}{2} \\ &\Rightarrow 3.1=\frac{k}{2} \quad\left[\frac{\sin x}{x}=1 \therefore \frac{\sin 3 x}{3 x}=1\right] \end{aligned}

Hence, k = 6

So, the correct option is (b)

Posted by

Gurleen Kaur

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