# Math Help - one-sided limits

1. ## one-sided limits

lim x-->2- (-4x^3+1/x-2)

find the limit as x approaches 2 from the left.

Thanks!

2. Originally Posted by kristenstemmer
lim x-->2- (-4x^3+1/x-2)

find the limit as x approaches 2 from the left.

Thanks!
Just making sure...is it $\lim_{x\to2^-}\frac{-4x^3+1}{x-2}$?

3. Yes, that is correct. Sorry, I don't know how to make it look like that

4. Originally Posted by Chris L T521
Just making sure...is it $\lim_{x\to2^-}\frac{-4x^3+1}{x-2}$?
Take note of the following:

As we get closer to 2 from the left, $-4x^3+1$ gets closer and closer to $-31$, but $x-2$ approaches "negative" zero.
This implies that the ratio $\frac{-4x^3+1}{x-2}$ approaches $+\infty$.

Thus, $\lim_{x\to2^-}\frac{-4x^3+1}{x-2}=+\infty$