2.12.25 Asymptotic Analysis

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