Need help on solving Limits.

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December 16th 2010, 05:09 AM
saykhong

Need help on solving Limits.

How to solve, lim x--->0 x/ln(1+x). Thanks in advance!\

Say Khong
God Bless.
December 16th 2010, 05:39 AM
SammyS

L'Hôpital's Rule

Quote:

Originally Posted by saykhong

How to solve, lim x--->0 x/ln(1+x). Thanks in advance!\

Say Khong
God Bless.

Limit is of the form: 0/0.

Use L'Hôpital's rule.
December 16th 2010, 06:02 AM
Archie Meade

Quote:

Originally Posted by saykhong

How to solve, lim x--->0 x/ln(1+x). Thanks in advance!\

Say Khong
God Bless.

$\displaystyle\ y=\frac{1}{x}\Rightarrow\ x\rightarrow\ 0,\;\;\;y\rightarrow\infty$

$\displaystyle\lim_{y \to \infty}\frac{1}{y\;ln\left[1+\frac{1}{y}\right]}=\lim_{y \to \infty}\frac{1}{ln\left[1+\frac{1}{y}\right]^y}=\frac{1}{ln(e)}=1$

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