A book I am reading (Hoy et al.) states that the remainder in the Taylor expansion around $x=x_0$ is given by $f^n(x_0)(x_1-x_0)^n/n!$. However, in an example on exponential function expansion, the remainder is mentioned as $\xi^n/n!$, where $ \xi \in (0,x)$.
This doesn't reconcile with the remainder mentioned previously. I can't find an errata sheet and some of the answers in the exercises also use the same remainder. Is there something I am missing or is this a legit error?
The remainder is $f^{(n)}(\xi)(x_1-x_0)^n/n!$, with $\xi$ between $x_0$ and $x_1$.