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

Question

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

anonymous · Answer

The top part can be written as: (x+2)(x^2-2x+4)
Then we see that the (x+2) terms cancel out leaving you with:
(x^2-2x+4). Now i am sure you can compute that limit.

anonymous · Answer

not cancel out, i mean divide out

anonymous · Answer

we can also use L'Hôpital's rule
and differentiate both statements and we get 
3x^2/1=3x^2=12

jamesj · Answer

Why use a gun when you can use a finger?

anonymous · Answer

what?

jamesj · Answer

I'm saying that using l'Hopital's rule is a bit over the top here.

anonymous · Answer

okay then why would you mention it

jamesj · Answer

@Lagrange, I don't think you're following me.  I'm saying your method is better here than Noureldin's proposition.

zarkon · Answer

I love using a sledgehammer to pound in a nail. :)

anonymous · Answer

as in "why use an elephant gun to kill and ant"
point is that since you have a rational function and replacing x by -2 gives 0/0 tells you that it MUST factor as 
$$\frac{(x+2)\times \text{something}}{x+2}$$

anonymous · Answer

in other words if you want 
$$\lim_{x\rightarrow a}\frac{P(x)}{Q(x)}$$ for polynomials P and Q and you find that 
$$P(a)=Q(a)=0$$ the both numerator and denominator MUST factor as 
$$(x-a)\times \text{stuff}$$ but the factor theorem.

anonymous · Answer

*by