The value of $\underset{x→0}{\lim}\{(1+x)^{2/x}\}$ (where, {.} denotes fractional part of x) is:

$e^2-7$ $e^2-8$ $e^2-6$ None of these

$e^2-7$

Here, $\underset{x→0}{\lim}\{(1+x)^{2/x}\}$ $\underset{x→0}{\lim}\{(1+x)^{2/x}\}=\{e^{\underset{x→0}{\lim}x\frac{2}{x}}\}$ $=\{e^2\}=e^2-7$$\begin{bmatrix}∵e^2-(2.732)^2=7.463\\∴\{e^2\}=e^2-7\end{bmatrix}$