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$\lim_{x \to 0} {{(1 + x)}^{2 / x}}$ (where ${x}$ denotes fractional part of ${x}$ is equal to

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$e^{2} - 5$

$e^{2} - 8$

$e^{2} - 6$

$e^{2} - 7$

answer is D.

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Detailed Solution

${x} = x - [x]$ , $lim_{x \to 0} (1 + x)^{2 / x} - [lim_{x \to 0} (1 + x)^{2 / x}]$ $= e^{2} - [e^{2}] = e^{2} - 7$

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