washam13 |

Differentiability

washam13
washam13
Differentiability
Mar 16 2011, 6:45 PM EDT | Post edited: Mar 16 2011, 6:49 PM EDT
differentiable if fx(x0, y0) and fy(x0, y0) exist and


lim [delta f - fx(x0,y0)(delta x) - fy(x0,y0)(delta y)] / sqrt( (delta x)^2 + (delta y)^2 ) = 0

delta x --> 0 delta y --> 0
if differentiable, then continuous

Differentials:
dz = fx(x0,y0)dx + fy(x0,y0)dy l
dW = fx(x0,y0,z0)dx + fy(x0,y0,z0)dy + fz(x0,y0,z0) l total differential of F
delta f is approximated to df
delta z is approximated to dz

Local linear approximation
L(x,y) = f(x0,y0) + fx(x0,y0)(x-x0) + fy(x0,y0)(y-y0)
Do you find this valuable?    
Sign in to be the first to reply.