2.7.53 Function Properties

Condition: to find the most polych degree of degree \ (g (x) \) such that the function \ (f (x) \) is: 1) continuously differently differentiated on the entire line, if \ [f (x) = \ left \ {\ begin {array} \ frac {5 x} {4+x^{2}}, & | x | \ GEQ 1 \\ G (X), & | X | <1 \ END {Array} \ RIGHT. \]