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  • Please solve RD Sharma class 12 chapter 8 Continuity exercise Fill in the blanks question 17 maths textbook solution

Please solve RD Sharma class 12 chapter 8 Continuity exercise Fill in the blanks question 17 maths textbook solution

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best_answer

Answer: 6

Hint: f(x) is continuous when LHL=RHL

Given: f(x)=\left\{\begin{array}{c} \frac{\sin 3 x}{x}, \text { if } x \neq 0 \\ \frac{k}{2}, \text { if } x=0 \end{array}\right.

Solution:

            f(x)=\left\{\begin{array}{c} \frac{\sin 3 x}{x}, \text { if } x \neq 0 \\ \frac{k}{2}, \text { if } x=0 \end{array}\right.is continuous at x=0

            At x=0

             LHL=RHL =f(a)

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

            \begin{aligned} &3(1)=\frac{k}{2} \\ &k=6 \end{aligned}

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