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 March 28th, 2012, 09:15 PM #1 Member   Joined: Feb 2012 Posts: 42 Thanks: 0 finding the limit (e function) Hello, regarding finding the limit of this function: e^(5+x)-e^5 / x as x tends towards 0 I know the answser is e^5. My question is how would I show the working to solve this problem. All I did was test values closer to zero. Is that all I should show for the working or should I have used a formula or some other procedure ? Thanks
 March 28th, 2012, 09:19 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: finding the limit (e function) Have you been introduced to L'Hôpital's rule?
 March 28th, 2012, 10:29 PM #3 Member   Joined: Feb 2012 Posts: 42 Thanks: 0 Re: finding the limit (e function) Oh great, thanks for that. so using l'Hopital's rule: e^(5+h)-e^5 / 1 = 0/1 = limit of 0
March 29th, 2012, 04:28 AM   #4
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Re: finding the limit (e function)

Quote:
 Originally Posted by fran1942 Oh great, thanks for that. so using l'Hopital's rule: e^(5+h)-e^5 / 1 = 0/1 = limit of 0
$\lim_{x\to 0 }\frac{e^{x+5}-e^{5}}{x}=\lim_{x\to 0 }\frac{\left(e^{x+5}-e^5\right)'}{x#39;}=\lim_{x\to 0} e^{x+5}=e^{5}$

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