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  • Please solve RD Sharma class 12 chapter 9 Differentiability exercise Very short answer type question 13 maths textbook solution

Please solve RD Sharma class 12 chapter 9 Differentiability exercise Very short answer type question  13 maths textbook solution

Answers (1)

Answer : \frac{4}{5}

Hint: If f(x) is differentiable at x=4 then \lim _{x \rightarrow 4} \frac{f(x)-f(4)}{x-4}=f^{\prime}(4)

Given: \mathrm{f}(\mathrm{x})=\sqrt{x^{2}+9}

Explanation:  Asf(x) is differentiable at x=4

\begin{aligned} &\lim _{x \rightarrow 4} \frac{f(x)-f(4)}{x-4}=f^{\prime}\\\\ &\lim _{x \rightarrow 4} \frac{\sqrt{x^{2}+9}-\sqrt{4^{2}+9}}{x-4}=f^{\prime}\\\\ &\lim _{x \rightarrow 4} \frac{\sqrt{x^{2}+9}-5}{x-4}=f^{\prime}(4)\\ &\lim _{x \rightarrow 4} \frac{2 x}{2 \sqrt{x^{2}+9}}=f^{\prime} \text { (4) } \quad \text { [L-Hospital Rule] } \end{aligned}

\begin{aligned} &\frac{4}{\sqrt{16+9}}=f^{\prime} \\\\ &\frac{4}{5}=f^{\prime}(4) \end{aligned}

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