If $f(x) = \left\{ \begin{array}{r} x\sin\frac{1}{x},\ \ x
eq 0 \ k,\ \ \ \ \ \ \ \ \ \ \ x = 0 \end{array} ight.\$ is continuous at $x = 0$, then the value of $k$ is

Question

If $f(x) = \left\{ \begin{array}{r} x\sin\frac{1}{x},\ \ x 
eq 0 \ k,\ \ \ \ \ \ \ \ \ \ \ x = 0 \end{array} ight.\$ is continuous at $x = 0$, then the value of $k$ is

Dr. Abubacker · Accepted Answer

(c)
If function $f(x)$ is continuous at $x = 0$, then
$f(0) = \lim_{x ightarrow 0}{f(x)}$
$	herefore\ \ \ f(0) = k = \lim_{x ightarrow 0}{x\sin\frac{1}{x}}$
$\Rightarrow k = 0$ $\left\lbrack \because - 1 \leq \sin\frac{1}{x} \leq 1 ightbrack$

Q. If $f(x) = \left\{ \begin{array}{r} x\sin\frac{1}{x},\ \ x \neq 0 \\ k,\ \ \ \ \ \ \ \ \ \ \ x = 0 \end{array} \right.\$ is continuous at $x = 0$, then the value of $k$ is

Explanation

Reviewed by Dr. Abubacker

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