Problem 8.1.4. Prove Theorem 8.1.1. Theorem 8.1.1. Taylor's serles ythere exists a real number B such that |f(n+1) (t)|

Extracted text: Problem 8.1.4. Prove Theorem 8.1.1. Theorem 8.1.1. Taylor's serles ythere exists a real number B such that |f(n+1) (t)| < bwarnovegine="" megen="" n="" for="" ali="" nonnegative="" integers="" tn="" and="" for="" on="" l="" on="" an="" intervol="" containing="" a="" and="" c.="" then="" f(n+1)="" (t)(x="" –="" –="" t)"="" dt="" )="0" lim="" n00="" n!="" and="" so="" f(m)="" (a)="" f(x)="" -(x="" –="" a)".="" n!="" |="" n="0" in-context="" hint.="" you="" might="" want="" to="" use="" problem="" 7.4.8="" of="" chapter="" 7.="" also="" there="" are="" two="" cases="" to="" consider:="" a="">< x="" and="" x="">< a="" (the="" case="" x="a" is="" trivial).="" you="" will="" find="" that="" this="" is="" true="" in="" general.="" this="" is="" why="" we="" will="" often="" indicate="" that="" t="" is="" between="" a="" and="" x="" as="" in="" the="" theorem.="" in="" the="" case="" x="">< a.="" notice="" that="" a="" f(n+1)="" (t)(x="" –="" t)"="" dt="" t="Da" t%3dx="|/" fln+1)(t)(t="" –="" æ)"="">