Question

The value of k which makes \[f\left( x \right) = \begin{cases}\sin\frac{1}{x}, & x \neq 0 \\ k , & x = 0\end{cases}\]    continuous at x = 0, is

 

Options

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Answer 1

 none of these 

If   \[f\left( x \right)\]  is continuous at \[x = 0\] , then 

\[\lim_{x \to 0} f\left( x \right) = f\left( 0 \right)\]
\[ \Rightarrow \lim_{x \to 0} \left( \sin\frac{1}{x} \right) = k\]
\[ \text{ [But} \lim_{x \to 0} \left( \sin\frac{1}{x} \right) \text{ does not exist . Thus, there does not exist any k that makes }  f\left( x \right) \text{ a continuous function .} \]