What is the limit as x -> ∞ of (x^2 + 2) / (x - 1)?

1 Answer
Feb 3, 2016

This function diverges; the limit is 'equal' to oo.

Explanation:

Divide both the numerator and the denominator by x, that makes it easier.
lim_(n to oo) (x^2/x+2/x)/(x/x-1/x)=lim_(n to oo)(x+2/x)/(1-1/x)

We know that lim_(n to oo) 1/x=0, so
lim_(n to oo)(x+2/x)/(1-1/x)=lim_(n to oo)(x+0)/(1-0)=lim_(n to oo)(x)/(1)=lim_(n to oo)x=oo