Đáp án:
\(\lim\limits_{x\to 0}\dfrac{2- \sqrt{4-x}}{x}=\dfrac14\)
Giải thích các bước giải:
\(\begin{array}{l}
\quad \lim\limits_{x\to 0}\dfrac{2- \sqrt{4-x}}{x}\\
= \lim\limits_{x\to 0}\dfrac{\left(2- \sqrt{4-x}\right)\left(2+ \sqrt{4-x}\right)}{x\left(2+ \sqrt{4-x}\right)}\\
= \lim\limits_{x\to 0}\dfrac{4 - (4-x)}{x\left(2+ \sqrt{4-x}\right)}\\
= \lim\limits_{x\to 0}\dfrac{x}{x\left(2+ \sqrt{4-x}\right)}\\
= \lim\limits_{x\to 0}\dfrac{1}{2+ \sqrt{4-x}}\\
= \dfrac{1}{2 + \sqrt{4-0}}\\
= \dfrac{1}{4}
\end{array}\)
