# Thread: Find the limit algebraically

1. ## Find the limit algebraically

We're doing limits, which is pretty much the first thing you do in any cal class, but I can't rename this one to make it work. I think I'm going to have to find the derivative of the function, but we haven't learned that yet.

Lim(x--> 0) $((1/(2+x)) - (1/2))/x$

P.S. Sorry if the I don't know how to use the math format for this stuff. I'm new to this forum, and I don't know how to use the different tags

2. Originally Posted by TenaciousE
We're doing limits, which is pretty much the first thing you do in any cal class, but I can't rename this one to make it work. I think I'm going to have to find the derivative of the function, but we haven't learned that yet.

Lim(x--> 0) $((1/(2+x)) - (1/2))/x$

P.S. Sorry if the I don't know how to use the math format for this stuff. I'm new to this forum, and I don't know how to use the different tags
$\dfrac{\left[ \dfrac{1}{2+x}-\dfrac{1}{2}\right]}{x}=\dfrac{\left[ \dfrac{2-(2+x)}{2(2+x)}\right]}{x}=\dfrac{\left[ \dfrac{x}{2(2+x)}\right]}{x}=\dfrac{1}{2(2+x)}$

etc

CB

3. Thanks! Now, just out of curiosity, how would you solve with L'hopital's rule?

4. Originally Posted by TenaciousE
Thanks! Now, just out of curiosity, how would you solve with L'hopital's rule?
Since you have not done derivatives yet there is no point.

CB