Final Answer
0
Step-by-step Solution
Specify the solving method
1
Evaluate the limit $\lim_{x\to\infty }\left(\frac{x^x}{e^x}\right)$ by replacing all occurrences of $x$ by $\infty $
$\frac{\infty ^{\infty }}{e^{\infty }}$
2
Apply the formula: $\infty ^{\infty }$$=\infty $
$\frac{\infty }{e^{\infty }}$
3
In the fraction $\frac{\infty }{e^{\infty }}$, as the expression of the denominator grows faster than the numerator, the quotient approaches $0$
0
Final Answer
0