Cho hàm số f ( x ) = { 3 − √ 4 − x k h i x ≠ 0 1 k h i x = 0 . Khi đó f′(0) là kết quả nào sau đây?

Lời giải

\[{\rm{f'}}\left( 0 \right) = \mathop {\lim }\limits_{{\rm{x}} \to 0} \frac{{{\rm{f}}\left( {\rm{x}} \right) - f\left( 0 \right)}}{{{\rm{x}} - 0}} = \mathop {\lim }\limits_{{\rm{x}} \to 0} \frac{{3 - \sqrt {4 - {\rm{x}}} - 1}}{{\rm{x}}} = \mathop {\lim }\limits_{{\rm{x}} \to 0} \frac{{2 - \sqrt {4 - {\rm{x}}} }}{{\rm{x}}} = \mathop {\lim }\limits_{{\rm{x}} \to 0} \frac{{4 - 4 + {\rm{x}}}}{{{\rm{x}}\left( {2 + \sqrt {4 - {\rm{x}}} } \right)}}\]

\[ = \mathop {\lim }\limits_{{\rm{x}} \to 0} \frac{1}{{2 + \sqrt {4 - {\rm{x}}} }} = \frac{1}{4}\]