Question

If $f\left(x\right)=e^x$, then $\underset{x\to 0}{lim}f\left(f\right(x){)}^{\frac{1}{\left(f\right(x\left)\right)}}$ is equal to (where $\left\{x\right\}$ denotes fractional part of $x$).

• A. $f\left(1\right)$
• B. $f\left(0\right)$
• C. $0$
• D. Does not exist

Answer 1

The correct option is A $f\left(1\right)$

$\underset{x\to 0}{lim}f\left(f\right(x){)}^{\frac{1}{f\left(x\right)}}=\underset{x\to 0}{lim}{e}^{e^x\times e^{-x}}$

$=\underset{x\to 0}{lim}{e}^1$

$=e^1$

$=f\left(1\right)$