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  • Please solve RD Sharma class 12 chapter Continuity exercise 8.2 question 10 maths textbook solution

Please solve RD Sharma class 12 chapter Continuity exercise 8.2 question 10 maths textbook solution

Answers (1)

Answer:

everywhere continuous.

Hint:

 sine function is everywhere continuous.

Given:

 f(x)=sin(x)

Explanation:

f(x)= \begin{cases}\sin x & x \geq 0 \\ \sin (-x) & x<0\end{cases}

= \begin{cases}\sin x & x \geq 0 \\ -\sin x & x<0\end{cases}

As sine function is everywhere continuous &

\begin{aligned} &\lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0}-\sin 0=0 \\ &\text { and } \\ &\lim _{x \rightarrow 0^{+}} f(x)=\lim _{x \rightarrow 0} \sin 0=0 \\ &f(0)=\sin 0=0 \end{aligned}

Hence, f(x) is everywhere continuous.

Posted by

Gurleen Kaur

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