Cho hàm số

B

- Hướng dẫn giải

Đáp án B

Ta có $\underset{x\to 0}{\lim }f\left(x\right)=\frac{2\sqrt{1+x}-\sqrt[3]{8-x}}{x}=\underset{x\to 0}{\lim }\frac{2\sqrt{1+x}-\sqrt[3]{8-x}}{x}$

$\underset{x\to 0}{\lim }\frac{{\displaystyle \frac{2x}{\sqrt{1+x}+1}}-{\displaystyle \frac{x}{4+2\sqrt[3]{8-x}+\sqrt[3]{{\left(8-x\right)}^2}}}}{x}=\underset{x\to 0}{\lim }\left(\frac{2}{\sqrt{1+x}+1}+\frac{1}{4+2\sqrt[3]{8-x}+\sqrt[3]{{\left(8-x\right)}^2}}\right)=\frac{13}{12}$.