# Simple limit problem

• Oct 4th 2009, 06:09 AM
Greg98
Simple limit problem
Hello, this basic limit problem puzzles me:

$
\lim_{x\rightarrow \ -2} \frac{x-1}{x+2}
$

My intuition says, that there isn't limit on this spot, because I couldn't modify(tried factorize or divide with x etc.) expression to shape, where the function is defined. Graphing the function didn't help either. But, maybe there is some way...? Any help is appreciated, thanks!
• Oct 4th 2009, 06:14 AM
e^(i*pi)
Quote:

Originally Posted by Greg98
Hello, this basic limit problem puzzles me:

$
\lim_{x\rightarrow \ -2} \frac{x-1}{x+2}
$

My intuition says, that there isn't limit on this spot, because I couldn't modify(tried factorize or divide with x etc.) expression to shape, where the function is defined. Graphing the function didn't help either. But, maybe there is some way...? Any help is appreciated, thanks!

As x approaches -2 the denominator is getting closer to zero while the numerator is getting (slightly) more negative.

And we know what happens when we divide by an increasingly small denominator