- I$\displaystyle \lim x \rightarrow \infty$

$\displaystyle (e^{x} + x)^{\dfrac{9}{x}}$

$\displaystyle (e^{\infty} + \infty)^{\dfrac{9}{\infty}}$

$\displaystyle \infty^{0} $ndeterminate

OR

$\displaystyle \lim x \rightarrow \infty$

$\displaystyle x^{\dfrac{4}{x}}$

$\displaystyle \infty^{\dfrac{4}{\infty}}$

$\displaystyle \infty^{0}$= 1

Both problems involve infinity to the 0 power. But they come out differently. Why?