$\lim_{x \to I^{-}} \frac{e^{{x}} - {x} - 1}{{x}^{2}} =$ (when {.} is Fractional part of x ) and $I$ is an integer

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$\frac{I}{2}$

Does not exist

e-2

answer is B.

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Detailed Solution

$\{x\} = x - [x] x \to I^{-} \Rightarrow \{x\} = x - (I - 1) = x - I + 1$
$\lim_{x \to I^{-}} \frac{e^{{x}} - {x} - 1}{{x}^{2}} = \lim_{x \to I^{-}} \frac{e^{x - I + 1} - (x - I + 1) - 1}{{(x - I + 1)}^{2}} = e - 2$

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