Let \( f(x)=\left\{\begin{aligned} x \sin \frac{1}{x}, & \text { if } x \neq 0 \\ 0, \text { whe...

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Let \( f(x)=\left\{\begin{aligned} x \sin \frac{1}{x}, & \text { if } x \neq 0 \\ 0, \text { when } x=0 \end{aligned}\right. \)
Then, which of the following is the true statement?
(a) \( f(x) \) is not defined at \( x=0 \)
(b) \( \lim _{x \rightarrow 0} f(x) \) does not exist
(c) \( f(x) \) is continuous at \( x=0 \)
(d) \( f(x) \) is discontinuous at \( x=0 \)
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