Question

( x^2 + x +1) / (x-1) . find limit as x approaches 1

Answer 1

The limit does not exist. More accurately, the limit approaches \(-\infty\) as x approaches \(1^-\), and \(\infty\) as x approaches \(1^+\).

Answer 2

but can't you do anything with the numerator and get an answer other than infinity?

Answer 3

You can do that if the top and the bottom are both \(0\) when you plug \(x=1\). But this is not the case here. You can see that if you plug \(x=1\) in there, you get \(\frac{3}{0}\). That means that the limit is definitely approaching either \(-\infty\) or \(\infty\).

Answer 4

oh, thanks =)

Answer 5

You're welcome!