Cho biết lim x → x0 f ( x ) = 2 .Tính L = lim x → x0 căn bậc hai của (f ( x ) + 2) − f ( x )/ f ( x ) − 2

* Hướng dẫn giải

\[\begin{array}{*{20}{l}}{L = \mathop {\lim }\limits_{x \to {x_0}} \frac{{\sqrt {f\left( x \right) + 2} - f\left( x \right)}}{{f\left( x \right) - 2}}}\\{\,\,\,\,\, = \mathop {\lim }\limits_{x \to {x_0}} \frac{{f\left( x \right) + 2 - {f^2}\left( x \right)}}{{f\left( x \right) - 2}}.\frac{1}{{\sqrt {f\left( x \right) + 2} + f\left( x \right)}}}\\{\,\,\,\,\, = \mathop {\lim }\limits_{x \to {x_0}} \frac{{ - \left[ {f\left( x \right) + 1} \right]\left[ {f\left( x \right) - 2} \right]}}{{f\left( x \right) - 2}}.\frac{1}{{\sqrt {f\left( x \right) + 2} + f\left( x \right)}}}\\{\,\,\,\,\, = - \frac{3}{4}}\end{array}\]