Answer to Question #61735 in Differential Equations for Etinyene

Question

1. If u = f(x,y) be a function of two independent variables x and y, then ∂u/∂y is equal to
a) lim△x→0f(x+△x,y)−f(x,y)△x
b) lim△y→0f(x,y+△y)−f(x,y)△y
c) limy→0f(x,y+△y)−f(x,y)△y
d) lim△y→0f(x+△x,y)−f(x,y)△x
2. Find the total differential of the function
u=x2y−3y

a)2x+(x2−3)dy
b) 2xydx+x2dy
c) 2xydx+(x2−3)dy
d) 2xydx+(x3−2)dy
3. The total differential du of a function u (x, y) = 0 is defined as

a) ∂u∂xdx+∂u∂xdy=0
b) ∂u∂xdy+∂u∂xdy=0
c) ∂u∂xdx+∂u∂ydx=0
d)∂u∂xdx+∂u∂ydy=0