How do you find the limit [math]\displaystyle{ \lim_{x\to4} \tfrac{\sqrt{x-3}-1}{\sqrt{x}-2}}[/math] without l'Hôpital's rule?
What is [math]\displaystyle\lim_{x\to \infty}x^3(\sqrt {x^2+\sqrt {x^4+1}}-x\sqrt {2})[/math]?