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  • Provide solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 2

Provide solution for RD Sharma maths class 12 chapter Continuity exercise 8.2 question 2

Answers (1)

Answer:

 Discontinuous at x = 0.

Hint:

 If a function is not continuous at one point then it is discontinuous. As at that point

\lim _{x \rightarrow a^{-}} f(x) \neq \lim _{x \rightarrow a^{+}} f(x) \neq f(0)

and this is the definition of discontinuity.

Given:

 f(x)= \begin{cases}\frac{x}{|x|} & x \neq 0 \\ 0 & x=0\end{cases}

Explanation:

Now consider 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{-h}{-h \mid}=-1 \\ &\text { R.H.L } \lim _{x \rightarrow 0^{-}} f(x)=\lim _{h \rightarrow 0}(0+h)=\lim _{h \rightarrow 0} \frac{h}{|h|}=1 \end{aligned}

So

L.H.S \neq R.H.L

Function is discontinuous at X = 0

Posted by

Gurleen Kaur

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