1. ## Limits Help

Hi,

I have just started a calulus class (i'm a high school senior) and we've been introduced to limits.

I am unsure of how to facor the following

$

lim (x^2+5x)/(x+4)

$

With the limit approaching zero.
I factored it to:

x(x+5)/(x+4)

and got a limit of zero. Is that the final answer or is there another way to get another value?

2. There's actually no need to factor here (although what you did is not wrong). When you substitute 0 in for x you get 0/4 which is 0. So the limit is 0.

3. Okay thanks.
I was kind of confused about whether or not the zero was indeed the limit.
Is the general rule that if you plug in the approaching value and you get 0/0, you have to factor further?

4. 0/c is just 0 as long as c is not 0.

0/0 is an indeterminate form. More work needs to be done to compute the limit. There isn't one technique that will work all the time, but if you have a rational function (a quotient of polynomials), then the factoring technique you're talking about will always work.