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