\(\lim\limits_{x\rightarrow2}\dfrac{f\left(x\right)-1}{x-2}=4\rightarrow\lim\limits_{x\rightarrow2}\left[f\left(x\right)-1\right]=0\rightarrow\lim\limits_{x\rightarrow2}f\left(x\right)=1\)
Do \(\lim\limits_{x\rightarrow2}\left[\sqrt{f\left(x\right)+2x+1}-\sqrt[3]{4+2x}\right]=\sqrt{1+2.2+1}-\sqrt[3]{4+2.1}>0\\ \lim\limits_{x\rightarrow2}\left(x^2-4\right)=0\)
Suy ra \(I=+\infty\)