# Thread: calculating limit of rational function

1. ## calculating limit of rational function

I'm not sure what to do when I plug in "a" in a rational function if the numerator comes out as zero, here is the problem:

lim (x+2)/(x^3+8)
x--> -2

the answer in the back is 1/12, could someone help me see how to find this?

Thx!!!

2. The thing is you got a fraction here:

$\displaystyle \frac {x+2} {x^3 + 8}$

where if you put x = -2 in, both the top and the bottom are zero.

So what you do is you factorise the bottom, and you'll see that it has a factor of x+2. So divide top and bottom by x+2 and see what you're left with.

3. Originally Posted by Matt Westwood
The thing is you got a fraction here:

$\displaystyle \frac {x+2} {x^3 + 8}$

where if you put x = -2 in, both the top and the bottom are zero.

So what you do is you factorise the bottom, and you'll see that it has a factor of x+2. So divide top and bottom by x+2 and see what you're left with.
to piggy back on this excellent advice, think "sum of two cubes"

4. oh ok, I should have seen that, lol. thx!

(x+2)/(x^2+4)(x+2) = 1/12 x--> -2

5. Originally Posted by calcnewbie
oh ok, I should have seen that, lol. thx!

(x+2)/[(x^2 - 2x +4)(x+2)] = 1/12 x--> -2
see the correction above. somehow you got the right answer when you had the wrong factorization i don't see how, you must've mistyped