# Confusing Answers

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• Nov 4th 2013, 11:23 PM
Jason76
Confusing Answers
Quote:

$\lim x \rightarrow \infty$

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

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

$\infty^{0}$
- Indeterminate
OR

Quote:

$\lim x \rightarrow \infty$

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

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

$\infty^{0}$
= 1

Both problems involve infinity to the 0 power. But they come out differently. Why?
• Nov 4th 2013, 11:27 PM
chiro
Re: Confusing Answers
Hey Jason76.

Basically the things inside the parentheses grow at different rates in relation to 9/x as x -> infinity.

I'd suggest you look at how the exponential function is defined in terms of limits and compare that with your x^(0) as x -> infinity as this will give you a better way of answering your own question.