How to take the derivative of this function

  • Thread starter JKLM
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  • #1
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Main Question or Discussion Point

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
 

Answers and Replies

  • #2
mathman
Science Advisor
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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.
 
  • #3
650
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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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