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  • Explain solution RD Sharma class 12 chapter 8 Continuity exercise multiple choice question 48 maths

Explain solution RD Sharma class 12 chapter 8 Continuity exercise multiple choice question 48 maths

Answers (1)

Answer:

 The correct option is (b)

Hint:

 Standard limit:

\begin{aligned} (i) \lim _{x \rightarrow 0} \frac{\sin x}{x}=1 \\ (ii) \lim _{x \rightarrow 0} \cos x=1 \end{aligned}

Given:

 f(x)=\left\{\begin{array}{cl} \frac{\sin x}{x}+\cos x &, \text { if } x \neq 0 \\ k & , \text { if } x=0 \end{array}\right.

 f(x) is continuous at x = 0.

So,

\begin{aligned} &=\lim _{x \rightarrow 0} f(x)=f(0) \\ &=\lim _{x \rightarrow 0}\left(\frac{\sin x}{x}+\cos x\right)=k \\ &=\lim _{x \rightarrow 0} \frac{\sin x}{x}+\lim _{x \rightarrow 0} \cos x=k \\ &=1+1=k \\ &=k=2 \end{aligned}

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Gurleen Kaur

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