$lim x \to a^{-} {\frac{| x |^{3}}{a} - [\frac{x}{a}]^{3}}, a > 0$ where $[x]$ denotes the greatest integer less than or equal to $x$ , is:

a^{2} - 3

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a^{2} - 1

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a^{2}

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a

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Solution

The correct option is C $a^{2}$
For $x \to a^{-},$
$0 < \frac{x}{a} < 1$
Thus, $[\frac{x}{a}] = 0$
The given question reduces to
${lim}_{x \to a^{-}} \frac{{| x |}^{3}}{a}$
$= \frac{a^{3}}{a} = a^{2}$

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