# Calculating Limit of Function – A function to the power of a function – Exercise 555

### Exercise

Evaluate the following limit:

$$\lim _ { x \rightarrow \infty} { ( 1 +2 e^{-x} ) }^{e^x + x}$$

$$\lim _ { x \rightarrow \infty} { ( 1 +2 e^{-x} ) }^{e^x + x}=e^2$$