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  • Explain solution RD Sharma class 12 chapter 8 Continuity exercise multiple choice question 36 maths

Explain solution RD Sharma class 12 chapter 8 Continuity exercise multiple choice question 36 maths

Answers (1)

Answer:

 The correct option is (d)

Hint:

(i) A function f(x) is said to be continuous at a point x = a of its domain, if

\begin{aligned} &\lim _{x \rightarrow a} f(x)=f(a) \\ &\lim _{x \rightarrow a^{+}} f(a+h)=\lim _{x \rightarrow a^{-}} f(a-h)=f(a) \end{aligned}

(ii) Standard limits

\begin{aligned} &\lim _{x \rightarrow 0} \frac{\sin x}{x}=1 \\ \end{aligned}

Given:

 \begin{aligned} f(x)=\sin \frac{1}{x} \end{aligned}

Solution:

\begin{aligned} f(x)=\sin \frac{1}{x} \end{aligned}

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

Function f(x) is continuous at x = 0

\begin{aligned} &\lim _{x \rightarrow 0} f(x)=f(0) \\ &\lim _{x \rightarrow 0} \sin \frac{1}{x}=k \end{aligned}

Value does not exist for fraction to be continuous.

So, the option (d) is correct.

Posted by

Gurleen Kaur

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