2.12.25 Asymptotic analysis

Condition: Determine whether the functions \( f_{1}(x) \) and \( f_{2}(x) \) are infinitesimal or infinitely large for \( x \rightarrow x_{0} \). Select the main parts of the functions \( f_{1}(x) \) and \( f_{2}(x) \). Determine the order of the functions with respect to \(x\). Compare features. \[ \begin{array}{l} f_{1}(x)=\sin \left(x \sqrt{x}+e^{2 x}-1\right) \\ f_{2}(x)=\sqrt{x} \tan \sqrt[3]{x}, \quad x_{0}=0 \end{array} \]