Tính giới hạn I = Lim {2x + 1}  + căn [3]x + 1}} - 2}/ {x

\({I_1} = \mathop {\lim }\limits_{x \to 0} \frac{{\sqrt[3]{{x + 1}} - 1}}{x} = \mathop {\lim }\limits_{x \to 0} \frac{1}{{\sqrt[3]{{{{\left( {x + 1} \right)}^2}}} + \sqrt[3]{{x + 1}} + 1}} = \frac{1}{3}\)

 \({I_2} = \mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {2x + 1} - 1}}{x} = \mathop {\lim }\limits_{x \to 0} \frac{2}{{\sqrt {2x + 1} + 1}} = 1\)

\( \Rightarrow I = {I_1} + {I_2} = \frac{4}{3}.\)