Very simple limit problem

Sep 2011
8
0
i am not sure if i am posting in the right section anyway i have a problem that is driving me insane, basically i have solve a limit for -4 while the expression is -(9/x+4).

If i input -4 it will give me -9/0 which is wrong. The tip is that i need to do some algebraical modification to the expression, but i tried everything and it always gives me undefined. I appreciate your time...

Thank you
 
Jul 2011
1,254
389
Belgium
If I interpret your question correctly the limit you have to calculate is:
\(\displaystyle \lim_{x \to -4} \frac{-9}{x+4}\)

Have you ever seen that:
\(\displaystyle \lim_{x \to 0} \frac{a}{0}=\pm \infty\) (a>0 gives \(\displaystyle +\infty\), a<0 gives \(\displaystyle -\infty\))
?
 
Nov 2010
600
216
Northwest Arkansas
\(\displaystyle \lim_{x \to -4} -\frac{9}{x + 4}\) ?

That limit doesn't exist.

Some limits with, for example, "9/0" would be considered "infinity", in the extended sense. But your example tends to +/- infinity, depending on the approach.