詳解：極限值=函數值

\(a = \lim \limits_{x \to 0} \frac{{\sqrt {x + 16}  - \sqrt {16 - x} }}{x}{\rm{ = }}\lim \limits_{x \to 0} \frac{{{\rm{(}}\sqrt {x + 16}  - \sqrt {16 - x} {\rm{)(}}\sqrt {x + 16} {\rm{ + }}\sqrt {16 - x} {\rm{)}}}}{{x{\rm{(}}\sqrt {x + 16} {\rm{ + }}\sqrt {16 - x} {\rm{)}}}}\)\

\( = \lim \limits_{x \to 0 } \frac {(x+16) – (16-x)}{x(\sqrt{x+16} + \sqrt {16-x}} = \lim \limits_{x \to 0 } \frac {2x}{x(\sqrt{x+16} + \sqrt {16-x}} =\lim \limits_{x \to 0 } \frac {2}{x(\sqrt{x+16} + \sqrt {16-x}} = \frac {1}{4} \)