Need help with limit problem

Question

find limit as x goes to infinity of(x² - sqrt(x²-16)

Answer 1

There is no limit, i.e. the difference is unbounded.

For purposes of this editor let a=sqrt(x²-16)

Multiply the original expression by (x²+a)/(x²+a).

Expand the numerator and you will see that the fraction approaches x² as x increases.