Question

#P2 The differential of surface area, ds, for a surface determined by the graph of z=f(x,y) is calculated by dS = #P3 The differential of surface area, dS, for a surface determined by the graph of x = f(y,z) is calculated by dS = #P4 True or false: If Fis a velocity vector field for some fluid and S is a semipermeable surface, then the flux integral JJs FindS computes how quickly volume is passing through the surface S.

Answer 1

- Salution: The differential determined by - calculated of the surface area, ds, for a surface graph of = f Cary) is as = ss 1 ² + fy 2 ts da where (x,y) and da is e point sueface from area the region element, da D. de dy for a x = (f {Y (2)] The differential of surface area, ds, sueface deleemined by the graph of is calculated by, as <= f (4,3) as = ss 1 fy² + f₂²+1 da 20 where and da cy,r) is is surface point area from the region D. element, dA= dy dz a True . For velocity rector suefaces, the Hua - SS Fonds on as semipermiable Field is given the volume of theid The crossing Hua as a cooss the per unit s as time.