Answer is: option3
\( 1+\frac{x}{3}-\frac{x^2}{9} \)Solution:
\[ f(x)=(1+x)^{1/3} \]
\[ f'(x)=\frac{1}{3}(1+x)^{-2/3},\qquad f''(x)=-\frac{2}{9}(1+x)^{-5/3} \]
\[ f(0)=1,\qquad f'(0)=\frac{1}{3},\qquad f''(0)=-\frac{2}{9} \]
\[ a_0=1,\qquad a_1=\frac{1}{3},\qquad a_2=\frac{f''(0)}{2!}=-\frac{1}{9} \]
\[ T_2(x)=1+\frac{x}{3}-\frac{x^2}{9} \]
