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How to take the derivative of this function

  1. Jan 20, 2004 #1
    What is the Lim as x approaches 0 of (1+sin(pi*x))^(1/x)
    I couldnt figure out how to take the derivative of this function
     
  2. jcsd
  3. Jan 20, 2004 #2

    mathman

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    Gold Member

    You don't need to take derivatives.

    As x->0, sin(pi*x) is approx pi*x. Your expression can be represented as exp(ln(1+pi*x)/x). Then ln(1+pi*x) is approx pi*x as x->0. The net result is exp(pi) is the limit that you want.
     
  4. Jan 20, 2004 #3
    for the derivative part take log
    say
    [tex]L = \lim_{x\rightarrow 0}[1+sin(\pi x)]^\frac{1}{x}[/tex]

    Take log
    [tex]logL = \lim_{x\rightarrow 0}\frac{log(1+sin\pi x)}{x}[/tex]
    I hope u can differentiate from there on

    Though mathman's reply is best u should do it that way
     
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