Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 4 / 28K / b / Solution

The Taylor theorem with Lagrange remainder supplies a point ${\xi }_i$ between $x_0$ and $X_i=x_0+h{Z}_i$ such thatSince $Z_i^2=1$ and $Y_i=g(X_i)+{\epsilon }_i$,