# Math Help - Finding the limit

1. ## Finding the limit

Hi guys i need some help in solving this question

the problem is:

lim -> 0

and the equation is:

((1/x+3) - (1/3))/x

if its too messy above, basically (1/x+3) - (1/3) are all divided by 'x'.

Obviously, if I sub x = 0 then the equation will give me 0/0, so can anyone show me how to solve this one I would greatly appreciate it.

thanks guys

2. $\lim_{x\to 0}\frac{\frac{1}{x+3}-\frac{1}{3}}{x}=\lim_{x\to 0}\frac{\frac{3-x-3}{3(x+3)}}{x}=$

$=\lim_{x\to 0}\frac{-x}{3x(x+3)}=\lim_{x\to 0}\frac{-1}{3(x+3)}=-\frac{1}{9}$

3. Originally Posted by red_dog
$\lim_{x\to 0}\frac{\frac{1}{x+3}-\frac{1}{3}}{x}=\lim_{x\to 0}\frac{\frac{3-x-3}{3(x+3)}}{x}=$

$=\lim_{x\to 0}\frac{-x}{3x(x+3)}=\lim_{x\to 0}\frac{-1}{3(x+3)}=-\frac{1}{9}$

Thanks!!!