Answer to Question #55792 in Calculus for JOSEPH

Question

8 Let f(x,y) be a real single-valued function of two independent variables x and y, then the partial derivatives of f(x,y) with respect to y is defined as
(A)lim dx→0 f(x+dx,y)−f(x,y)/dx (B) lim dx→0 f(x,y+dy)−f(x,y)/dy (C) lim dx→0 f(x+dx,y)−f(y,x)/dy (D) lim dx→0 f(x+dx,y+dy)−f(x,y)/dx
9 Let f(x,y) be a real single-valued function of two independent variables x and y, then the partial derivatives of f(x,y) with respect to x is defined as
(A) lim dx→0 f(x+dx,y)−f(x,y)/dx (B) lim dx→0 f(x+dx,y)−f(x,y)/dy (C) lim dx→0 f(x+dx,y)−f(y,x)/dx (D) lim dx→0 f(x+dy,y)−f(x,y)/dx

10 If f(x,y)=2x^3 +3y^2, find f(-1,-2)