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  • Provide solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 3 subquestion (iv)

Provide solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 3 subquestion (iv)

Answers (1)

Answer:

x = 0

Hint:

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

Given:

 f(x)= \begin{cases}\frac{\sin 3 x}{x} & x \neq 0 \\ 4 & x=0\end{cases}

Explanation:

At x = 0

\begin{aligned} &\text { L.H.L }=\lim _{x \rightarrow 0^{-}} f(x)=\lim _{h \rightarrow 0}(0-h)=\lim _{h \rightarrow 0} \frac{\sin 3(-h)}{-h} \\ &=\lim _{h \rightarrow 0} \frac{-\sin 3 \mathrm{~h}}{-h}=1 \\ &=\lim _{h \rightarrow 0} \frac{-3 \sin 3 \mathrm{~h}}{3 h}=3 \end{aligned}

\begin{aligned} &\text { R.H.L }=\lim _{x \rightarrow 0^{+}} f(x)=\lim _{h \rightarrow 0}(0+h)=\lim _{h \rightarrow 0} \frac{\sin 3 \mathrm{~h}}{h}=3 \\ &\text { Also } f(0)=4 \\ &\text { Thus L.H.L }=\text { R.H.L } \neq \mathrm{f}(0) \end{aligned}

\therefore f is not continuous at x = 0.

Posted by

Gurleen Kaur

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