Show that $\displaystyle lim_{x-->0}$ $\displaystyle ln (1+x)/x $ = 1 from the definition of derivative.

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- Jan 28th 2010, 03:58 PMwopashuiShow definition of derivative
Show that $\displaystyle lim_{x-->0}$ $\displaystyle ln (1+x)/x $ = 1 from the definition of derivative.

- Jan 28th 2010, 04:03 PMGeneral
- Jan 28th 2010, 05:52 PMwopashui
- Jan 28th 2010, 05:57 PMGeneral
I did not follow you!

$\displaystyle \frac{ln(1+x)}{x}=\frac{ln(1+x)-0}{x-0}$

Do you have problem in this one?

Substracting zero is allowed everywhere.

and I replaced $\displaystyle 0$ by $\displaystyle f(0)$

since $\displaystyle f(0)=ln(1+0)=ln(1)=0$

Please, explain more. - Jan 30th 2010, 11:22 AMwopashui