Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2012 / Paper 2 / 5

Near $x=2$, use $f(x)=2\ln x$, so $f^{\prime }(2)=1$ and $f^{\prime \prime }(2)=-1/2$. The Taylor series therefore beginsThe constant term is one of the requested three terms. The local expression $2\ln x$ is legitimate because this neighbourhood has $x>0$.