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  • Please solve RD Sharma class 12 chapter Continuity exercise 8.2 question 3 subquestion (iii) maths textbook solution

Please solve RD Sharma class 12 chapter Continuity exercise 8.2 question 3 subquestion (iii) maths textbook solution

Answers (1)

Answer:

 x = 0

Hint:

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

Given:

 f(x)= \begin{cases}\frac{\sin x}{x} & x<0 \\ 2 x+3 & x \geq 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 (-h)}{-h} \\ &=\lim _{h \rightarrow 0} \frac{-\sinh }{-h}=1 \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{\sinh }{h}=1 \\ &\text { Also } f(0)=2 \times 0+3=3 \\ &\text { Thus L.H.L}=\text {R.H.L} \neq \mathrm{f}(0) \end{aligned}

f is discontinuous at x = 0

Posted by

Gurleen Kaur

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