Tag: Remainder term

• Mean Value Theorems and Taylor's Theorem: Recovering a Function from Its DerivativesFrom the extreme value theorem we prove the mean value theorems of Rolle, Lagrange and Cauchy, then derive l'Hôpital's rule and Taylor's theorem with explicit error bounds.MathematicsCalculusUndergraduateMean value theoremTaylor expansionL'Hopital's ruleRemainder termAnalysis~26 min