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Limit of a function

  1. Jul 20, 2009 #1
    1. The problem statement, all variables and given/known data

    what is limit of (1+ax)^1/x w hen x → ∞ ????????????




    2. Relevant equations

    answer is e^a

    3. The attempt at a solution
    taking log i get
    log y=1/x log(1+ax)

    using l hospital i get

    logy=-1/x2 X a/1+ax
    so
    putting x->∞


    we get
    logy=0
    y=1
     
  2. jcsd
  3. Jul 20, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Oh! You mean (1+ ax)^(1/x)!

    You answer is correct.
    [tex]e^a= \lim_{x\rightarrow 0} (1+ ax)^{1/x}[/tex]

    That is, the limit as x goes to 0 not infinity.
     
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