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The function defined by $f (x) = \{\begin{cases} x \sin \frac{1}{x} for x \neq 0 \\ 0 for x = 0 \end{cases}$ at $x = 0$ is

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continuous

Discontinuous

Left continuous

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Correct option is A

Ltx→0 fx=Ltx→0 xsin1x=f0f is continuous at x=0

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The function defined by fx=xsin1x for x≠0 0 for x=0 at x=0 is

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The function defined by $f (x) = \{\begin{cases} x \sin \frac{1}{x} for x \neq 0 \\ 0 for x = 0 \end{cases}$ at $x = 0$ is