# Thread: limits with the e exponnent

1. ## limits with the e exponnent

I have trouble with these can anyone help me work out this problem.
lim e^((5x^2+sinx)/(x^2+20))
x-infinity

2. Originally Posted by macro
I have trouble with these can anyone help me work out this problem.
lim e^((5x^2+sinx)/(x^2+20))
x-infinity

ignore the exponent's base for a moment ... what is this limit?

$\displaystyle \lim_{x \to \infty} \frac{5x^2 + \sin{x}}{x^2 + 20}$

3. it's 5 right since its the principle term?

4. Originally Posted by macro
it's 5 right since its the principle term?
correct.

so, what is $\displaystyle \lim_{x \to \infty} e^{\frac{5x^2+\sin{x}}{x^2+20}}$ ?

5. Is the limit e^5 since its a constant?

6. Originally Posted by macro
Is the limit e^5 since its a constant?
yes, the limit is $\displaystyle e^5$ ... I don't know what you mean by "it's a constant"

the limit is just a property of composite functions ...

if $\displaystyle \lim_{x \to \infty} f(x) = 5$ , then $\displaystyle \lim_{x \to \infty} e^{f(x)} = e^5$

7. oh ok thanks a bunch

8. The crucial point is that $\displaystyle e^x$ is a continuous function:
$\displaystyle \lim_{x\to a}e^{f(x)}= e^{\lim_{x\to a} f(x)}$.