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Need help on proof

  1. Dec 13, 2003 #1
    Hi I need help again on my assignment, it's kindda hard...I did do what I could but I can't come up with anything@@" please help
    ***********
    Let F(x)=ln(x). We know that F'(x)=1/x. We will use this fact and the definition of derivatives to show that lim(n->inf) (1+1/n)^n=e
    a) Use the definition of the derivative to show that
    f'(1)=lim(h->0)(ln(1+h)/h)

    b)Show that (a) implies that
    ln[lim(h->0)(1+h)^1/h]=1

    c) Set h=1/h in (b) and let n-> inf Show that this implies
    lim(n->inf) (1+1/n)^n=e

    PLEASE HELP
     
  2. jcsd
  3. Dec 13, 2003 #2
    Apply the ab initio Rule for Derivative

    put x=1
    u will get first part

    now F'(1)=1/x=1

    u will get second part

    Set h=1/h in (b) and let n-> inf will give u
    third part of Q
     
  4. Dec 13, 2003 #3
    uhmmm...don't I suppose to "show" everything through a process until it reaches the final answer somewhat like a proof? cuz that's the way I understand the problem@@"
     
  5. Dec 13, 2003 #4
    Yes u have to

    its just hint which u yourself has quoted

    Anyway give your attempt as u will be giving in assignment
     
  6. Dec 13, 2003 #5
    uhmm....I did, but still don't know how....thanks anyways..I'll be discussing with my classmates thank you
     
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