- #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

I couldnt figure out how to take the derivative of this function

- Thread starter JKLM
- Start date

- #1

- 21

- 0

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

I couldnt figure out how to take the derivative of this function

- #2

mathman

Science Advisor

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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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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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