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

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

Answers (1)

Answer:

 Discontinuous at all integral points.

Hint:

 Greatest integer function is discontinuous at integral points.

Given:

 g(x)=x-[x]

Explanation:

g(x)=x-[x]

It is defined at all integral points

let n be an integer.

Then,

\begin{aligned} &g(n)=n-[n]=0\\ &\text { The left hand limit of } \mathrm{f} \text { at } \mathrm{x}=\mathrm{n} \text { is }\\ &\lim _{x \rightarrow n^{-}} g(x)=\lim _{x \rightarrow n^{n}}(x-[x])=\lim _{x \rightarrow n^{-}}(x)-\lim _{x \rightarrow n^{-}}[x]\\ &=n-(n-1)=1 \end{aligned}

\begin{aligned} &\text { The right hand limit of } f \text { at } x=n \text { is }\\ &\lim _{x \rightarrow n^{+}} g(x)=\lim _{x \rightarrow n^{+}}(x-[x])=\lim _{x \rightarrow n^{+}}(x)-\lim _{x \rightarrow n^{+}}[x]\\ &=n-n=0 \end{aligned}

\begin{aligned} &\text { L.H. } L \neq R . H . L\\ &\therefore g \text { is not continious at } x=n \end{aligned}

Hence g is discontinious at all integral points.

Posted by

Gurleen Kaur

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