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 September 9th, 2013, 03:31 PM #1 Newbie   Joined: Sep 2013 Posts: 3 Thanks: 0 Calculus Limits Lim x-> - infinity ((e^2x) -5)/ ((e^kx) +3) What should k be for the limit to exist? Hi can someone explain how to solve this to me? my teacher went through this in class but I just cant seem to understand what she's doing. Help!! :P
September 9th, 2013, 03:55 PM   #2
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Re: Calculus Limits

Quote:
 Originally Posted by ChanThar Lim x-> - infinity ((e^2x) -5)/ ((e^kx) +3) What should k be for the limit to exist? Hi can someone explain how to solve this to me? my teacher went through this in class but I just cant seem to understand what she's doing. Help!! :P
Since the form of the limit is $\frac{\infty}{\infty}$, we can use L'Hopital's rule. We have

$\lim_{x\to\infty}\frac{e^{2x}-5}{e^{kx}+3}=\lim_{x\to\infty}\frac{2e^{2x}}{ke^{k x}}$.

Can you continue?

 September 9th, 2013, 04:08 PM #3 Newbie   Joined: Sep 2013 Posts: 3 Thanks: 0 Re: Calculus Limits Oh yea i think I got it. I'll continue from there, thanks!

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lim tends to infinity 2^x -1

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