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  • Provide solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 11

Provide solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 11

Answers (1)

Answer:

 Everywhere continuous

Hint:

 sine function, polynomial function and identity are everywhere continuous.

Given:

 f(x)=\left\{\begin{array}{cc} \frac{\sin x}{x} & x<0 \\ x+1 & x \geq 0 \end{array}\right.

Explanation:

At x = 0

\begin{aligned} &f(0)=0+1=1 \\ &\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 \\ &\text { R.H.L } =\lim _{x \rightarrow 0^{+}} f(x)=\lim _{h \rightarrow 0}(0+h)=\lim _{h \rightarrow 0} h+1=1 \\ &\text { L.H.L } =\text { R.H.L }=f(0)=1 \end{aligned}

So, f(x) is everywhere continuous.

Posted by

Gurleen Kaur

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