IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Sciences => Topic started by: eightAs on January 01, 2010, 02:56:14 pm

Title: CIE P3 doubt ~
Post by: eightAs on January 01, 2010, 02:56:14 pm: I just came across a proof for the derivate of $e^x$ being $e^x$ itself.There was one part of the proof I couldn't understand. Why would the following equation hold:
$limit$ $(\LARGE\frac{e^x - 1}{x})$ $= 1$ .
Title: Re: CIE P3 doubt ~
Post by: astarmathsandphysics on January 01, 2010, 03:02:40 pm: l'hospital's rule
when f=g=0, use f/g=f'/g'
Title: Re: CIE P3 doubt ~
Post by: eightAs on January 01, 2010, 03:04:12 pm: Quote from: astarmathsandphysics on January 01, 2010, 03:02:40 pm
l'hospital's rule
when f=g=0, use f/g=f'/g'
Do you have notes on l'hospital's rule.
Title: Re: CIE P3 doubt ~
Post by: astarmathsandphysics on January 01, 2010, 03:08:13 pm: I will do a page on my website when I finish the big job on sunday
Title: Re: CIE P3 doubt ~
Post by: eightAs on January 01, 2010, 03:10:29 pm: Is there a proof without assuming the fact that the derivative of $e^x$ is $e^x$ itself.
Title: Re: CIE P3 doubt ~
Post by: astarmathsandphysics on January 01, 2010, 03:17:40 pm: Yes using taylor series
Title: Re: CIE P3 doubt ~
Post by: eightAs on January 01, 2010, 03:23:45 pm: Quote from: astarmathsandphysics on January 01, 2010, 03:17:40 pm
Yes using taylor series
Can you post it when you're free please.
Title: Re: CIE P3 doubt ~
Post by: astarmathsandphysics on January 01, 2010, 03:29:52 pm: Will post a link when I do that page of notes
Title: Re: CIE P3 doubt ~
Post by: astarmathsandphysics on January 07, 2010, 11:25:25 pm: http://www.astarmathsandphysics.com/university_maths_notes/calculus/university_maths_notes_calculus_lhospitals_rule.html
Title: Re: CIE P3 doubt ~
Post by: eightAs on January 12, 2010, 11:43:42 am: Thank you very much. :)
Title: Re: CIE P3 doubt ~
Post by: astarmathsandphysics on January 12, 2010, 11:47:39 am: No probs. Over the next few year I waim to write 8000 pages of maths notes.