Tìm giới hạn \(D=\lim\limits _{x \rightarrow 0} \frac{\sqrt[3]{x+1}-1}{\sqrt{2 x+1}-1}\)

* Hướng dẫn giải

Ta có 

\(D=\lim\limits _{x \rightarrow 0} \frac{x(\sqrt{2 x+1}+1)}{2 x\left[\sqrt[3]{(x+1)^{2}}+\sqrt[3]{x+1}+1\right]}=\lim \limits_{x \rightarrow 0} \frac{\sqrt{2 x+1}+1}{2\left[\sqrt[3]{(x+1)^{2}}+\sqrt[3]{x+1}+1\right]}=\frac{1}{3}\)