Hello.

I have to find the limit as x approaches 0 of the function

[ [(1/(3+x)] -(1/3) ] / x i tried direct substitution and to rationalize the denominator and numerator, but neither works...

what shoul i do?

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- May 23rd 2010, 07:21 PMguidol92A simple limit problem.
Hello.

I have to find the limit as x approaches 0 of the function

[ [(1/(3+x)] -(1/3) ] / x i tried direct substitution and to rationalize the denominator and numerator, but neither works...

what shoul i do? - May 23rd 2010, 07:30 PMProve It
$\displaystyle \frac{\frac{1}{3 + x} - \frac{1}{3}}{x} = \frac{\frac{3 - (3 + x)}{3(3 + x)}}{x}$

$\displaystyle = \frac{-\frac{x}{3(3 + x)}}{x}$

$\displaystyle = -\frac{1}{3(3 + x)}$.

So $\displaystyle \lim_{x \to 0}\left(\frac{\frac{1}{3 + x} - \frac{1}{3}}{x}\right) = \lim_{x \to 0}\left[-\frac{1}{3(3 + x)}\right]$

$\displaystyle = -\frac{1}{3(3)}$

$\displaystyle = -\frac{1}{9}$. - May 24th 2010, 12:51 AMmr fantastic