17.计算极限lim_(xto1)(sqrt(x+2)-sqrt(3))/(sqrt(x)-1).（8分）

将原式分子分母同时乘以共轭表达式，得 \[ \lim_{x \to 1} \frac{\sqrt{x+2} - \sqrt{3}}{\sqrt{x} - 1} = \lim_{x \to 1} \frac{(\sqrt{x+2} - \sqrt{3})(\sqrt{x+2} + \sqrt{3})}{(\sqrt{x} - 1)(\sqrt{x+2} + \sqrt{3})} = \lim_{x \to 1} \frac{x - 1}{(\sqrt{x} - 1)(\sqrt{x+2} + \sqrt{3})}. \] 注意到 $x - 1 = (\sqrt{x} - 1)(\sqrt{x} + 1)$，代入得 \[ \lim_{x \to 1} \frac{(\sqrt{x} - 1)(\sqrt{x} + 1)}{(\sqrt{x} - 1)(\sqrt{x+2} + \sqrt{3})} = \lim_{x \to 1} \frac{\sqrt{x} + 1}{\sqrt{x+2} + \sqrt{3}}. \] 当 $x \to 1$ 时，$\sqrt{x} \to 1$，$\sqrt{x+2} \to \sqrt{3}$，故 \[ \lim_{x \to 1} \frac{\sqrt{x} + 1}{\sqrt{x+2} + \sqrt{3}} = \frac{1 + 1}{\sqrt{3} + \sqrt{3}} = \frac{2}{2\sqrt{3}} = \frac{1}{\sqrt{3}}. \] **答案：** $\boxed{\frac{1}{\sqrt{3}}}$