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The value of $\mathrm{k}$ which makes $\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cl}\sin x & x \neq 0 \\ k & x=0\end{array}\right.$ continuous at $\mathrm{x}=0$, is
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$f(x)=\left\{\begin{array}{cl}\sin x, & x \neq 0 \\ k, & x=0\end{array}\right.$
Given, $\mathrm{f}(\mathrm{x})$ is continuous at $\mathrm{x}=0$
$\lim _{x \rightarrow 0} f(x)=f(0)$
$\Rightarrow \lim _{x \rightarrow 0} \sin x=k$
$\Rightarrow \mathrm{k}=0$
Given, $\mathrm{f}(\mathrm{x})$ is continuous at $\mathrm{x}=0$
$\lim _{x \rightarrow 0} f(x)=f(0)$
$\Rightarrow \lim _{x \rightarrow 0} \sin x=k$
$\Rightarrow \mathrm{k}=0$
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