]> L'Hôpital's

# L'Hôpital's Rule

Kevin Aylward B.Sc.

Overview

This paper provides a derivation of L'Hôpital's Rule.

L'Hôpital's Rule

Consider:

For the case of if f(x)=g(x)= then MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaabMgacaqGMbGaaeiiaiaadAgacaGGOaGaamiEaiaacMcacqGH9aqpcaWGNbGaaiikaiaadIhacaGGPaGaeyypa0JaeyOhIuQaaeiiaiaabshacaqGObGaaeyzaiaab6gaaaa@46BF@ , as above

the first terms of the denominator and numerator are 0

on taking the g(x) MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadEgacaGGOaGaamiEaiaacMcaaaa@392B@  limit first, thus