Posted by: pat June 28, 2006
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Here is a handout he gave it to me..................
he gave the complicated proof of e^x
I quote
" If the above proof seems intricate, consider the simpler but inexact "proof" below which is found in some calculus textsh...
Per the definition of derivative:
derivative of e^x =lim (e^(x+h)-e^x)/h = e^x lim (e^h-1)/h
h-o
now consider the heuristic argument that says for small h , e^h ~~ 1+h=h ( ~~ means "approx")
substituting we get
derivative of e^x = e^x lim ((1+h)-1)/h =e^x lim h/h = e^x
although tha above reasoning is appealing , consider the hidden flaw.......
we know derivative of a^x where a is constant =a^x ln a
but using the same method above we get,
derivative of a^x = a^x which is not true.."
4) Regarding the proof of e^x thing is concerned there are number of ways.
well loote if you can prove it then stop bi+ching around and just do the proof...I dont want any useless theory , speculations, smart a$$ comments ... just the proof