2006 Fall MATH 100 Lecture 101MATH 100 Lecture 10 Total Differential()()()()()()Total Differential:Consider ,,,Define total differential as ,,,,,,while the increment isΔ,,,,If is diff., thenxyzwfx y zdwfx y z dxfx y z dyfx y z dzwfxx yy zzfx y zfw==++=+ Δ+ Δ+ Δ−Δ=()()123123,,0 as ,,0,0,0dwxyzxyzεεεεεε+Δ +Δ +Δ→ΔΔΔ→
This preview has intentionally blurred sections.
Sign up to view the full version.
2006 Fall MATH 100 Lecture 102MATH 100 Lecture 10 Total DifferentialEx:Length, width & height of a box are measured with an error of at 5%, when they are used to calculate the diagonal, what is the maximal percentage error??knowwant towe%5Given :diagonaltheofLength :Solution222≤Δ≤++=DDzΔz,yΔy,xΔxzyxD