Question

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

Answer 1

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`