Question

How do you find the Limit of `[(x^2) - (2ln x)]` as x approaches infinity?

Answer 1

Factor out an `x^2`

Explanation:

`x^2-2lnx = x^2(1-(2lnx)/x^2)`

As `xrarroo`, we have `lnx/x^2 rarr 0`
(Treat this as a know limit or use l'Hospital's Rule.)

Therefore, as `x rarroo`, the product `x^2(1-(2lnx)/x^2)` increases without bound.

`lim_(xrarroo) (x^2-2lnx) = lim_(xrarroo)x^2(1-(2lnx)/x^2)`

`= oo`