Let $f (x) = x {(- 1)}^{[\frac{1}{x}]} . x \neq 0$ , where [x] denotes the greatest integer less than or equal to x. then $lim x \to 0 f (x)$

Does not exist

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is equal to 2

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is equal to 0

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is equal to -1

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Solution

The correct option is C
is equal to 0

Since [1/x] is an integer .
${(- 1)}^{[\frac{1}{x}]} = \pm 1$

Hence f(x)= $\pm x$
And $lim x \to 0 f (x)$ = 0

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