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need solution for RD Sharma maths class 12 chapter 8 Continuity exercise Very short answer question 11

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Answer: -3

Hint: \lim _{x \rightarrow 0} f(x)=f(0)

Given: f(x)is continuous at x=0 and

            Where f(x)=\left\{\begin{array}{l} \frac{k x}{|x|}, x<0 \\ 3, x \geq 0 \end{array}\right.


                    As f(x) is continuous at x=0 and

                    \lim _{x \rightarrow 0^{-}} f(x)=f(0)

                    \begin{aligned} &\lim _{x \rightarrow 0^{-}} \frac{k x}{|x|}=3 \\ &\text { As }|x|=-x \text { for } x<0, \\ &\Rightarrow \lim _{x \rightarrow 0} \frac{k x}{-x}=3 \\ &\Rightarrow-k=3 \\ &\Rightarrow k=-3 \end{aligned}

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