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  • Please solve RD Sharma class 12 chapter 8 Continuity exercise Very short answer question 5 maths textbook solution

Please solve RD Sharma class 12 chapter 8 Continuity exercise Very short answer question 5 maths textbook solution

Answers (1)

Answer: 10

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

Given: f(x)=\frac{\sin 10 x}{x}, x \neq 0   is continuous at x = 0

Explanation:

                As f(x)  is continuous at x = 0

                \begin{aligned} &=>\lim _{x \rightarrow 0} f(x)=f(0) \\ &=>\lim _{x \rightarrow 0} \frac{\sin 10 x}{x}=f(0) \\ &=>\lim _{x \rightarrow 0} \frac{10 \times \sin 10 x}{10 x}=f(0) \end{aligned}

                = > 10 \lim _{x \rightarrow 0} \frac{\sin 10 x}{10 x}=f(0) \; \; \; \; \; \; \; \; \; \; \; \; \quad\left[\lim _{x \rightarrow 0} \frac{\sin x}{x}=1\right]

                \begin{aligned} &=>10 \times 1=f(0) \end{aligned}

                \begin{aligned} \ = > f(0)=10 \end{aligned}

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