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