Expert: Paul Klarreich - 1/28/2008

Question
I can't figure out the limit for this one..

f(x)=(x^2-3x-10)/(x^2+10x+16)

lim as x approaches -2 from the left, f(x)=
lim as x approaches -2 from the right,f(x)=

It says error at -2, so I thought it was undefined but it says its wrong. This is the only one I cant get, I hope you can explain it to me. Thank you!

Answer
Questioner:   Aliya
Category:  Calculus
Private:  No
 
Subject:  limits
Question:  I can't figure out the limit for this one..

f(x)=(x^2-3x-10)/(x^2+10x+16)

lim as x approaches -2 from the left, f(x)=
lim as x approaches -2 from the right,f(x)=

It says error at -2, so I thought it was undefined but it says its wrong. This is the only one I cant get, I hope you can explain it to me. Thank you!
....................................
Hi, Aliya,

For starters, you might reduce the number of times you say 'it'.  That makes your conversation rather difficult to understand.

You want:

       x^2-3x-10
lim    ------------
x->-2   x^2+10x+16

Now you found that both top and bottom become zero at  x = -2.  [Yes, I said '=']

That means  x + 2 is a factor of both.  So:

       (x + 2)(x - 5)
lim    ---------------- =
x->-2   (x + 2)(x + 8)

       (x - 5)    -2 - 5     -7
lim    --------- = ------- = ----
x->-2   (x + 8)    -2 + 8      6

That's your limit. (From both left and right.)