chapter  3
26 Pages

Applications of differentiation

Thischapteraimstogivesomeideaofthetypesofapplicationin engineeringthatcanoccurfordifferentiation.Asindicatedin chapter1,dy/drisameasureoftherateatwhichyincreaseswith respecttox.Ifweconsideragraphofyplottedagainstxthen dyld.risthegradientofthegraphatapoint.Forexample,we mighthaveagraphshowinghowtheheightofliquidinacontainer varieswithtimeasaconsequenceofliquidenteringthrougha float-controlledvalve(figUre3.1).IfthechangeinheightisMina timel>tthenMll>tistheaveragerateofchangeofheightoverthe timeintervall>t.Inthelimitaswemakedtsmallerandsmallerso thatittendsto0,thenweendupwithwhatcanbeconsideredthe rateofchangeofheightwithtimedhldtataninstantoftime.