Chứng minh (x + y)^2 > = 4xy với x, y > 0
Tính lim.
\mathop {\lim }\limits_{x \to + \infty } \left( {\sqrt {x - 1} - \sqrt x } \right)
= \mathop {\lim }\limits_{x \to + \infty } \frac{{x - 1 - x}}{{\sqrt {x - 1} + \sqrt x }}
= \mathop {\lim }\limits_{x \to + \infty } \frac{{ - 1}}{{\sqrt {1 - \frac{1}{x}} + \sqrt 1 }}
= \mathop {\lim }\limits_{x \to + \infty } \frac{{\frac{{ - 1}}{{\sqrt x }}}}{{\sqrt {1 - 0} + 1}}
= 0.