Answer is: option2
\( (x-1)-\frac{1}{2}(x-1)^2+\frac{1}{3}(x-1)^3 \)Solution:
\[ f(x)=\ln x,\quad f'(x)=\frac{1}{x},\quad f''(x)=-\frac{1}{x^2},\quad f'''(x)=\frac{2}{x^3} \]
\[ f(1)=0,\quad f'(1)=1,\quad f''(1)=-1,\quad f'''(1)=2 \]
\[ a_0=0,\quad a_1=1,\quad a_2=-\frac{1}{2},\quad a_3=\frac{1}{3} \]
\[ T_3(x)=(x-1)-\frac{1}{2}(x-1)^2+\frac{1}{3}(x-1)^3 \]
