Recent content by freya81

it this correct 2. a) f is differentiable at (a,b) iff there exists a linear mapping L such that lim((f(a+h,b+k)-f(a,b)-L(h,k))/|(h,k)|,(h,k)->(0,0))=0. ∂f/∂x(a,b)=lim((f(a+h,b)-f(a,b))/h,h->0), and ∂f/∂y(a,b)=lim((f(a,b+k)-f(a,b))/k,k->0). does L=grad f; that is...

Am mainly stuck on parts c) and d) but thought i'd put in the other questions as an aid 2. a) Define what it means to describe a function f of two real variables as differentiable at (a, b)? Define (as limits) the partial derivatives df/dx and df/dy at (a, b) and prove that if f is...

1a)Do these functions have limits.If the limit exists, find it with justification, if not explain why not i) f(x,y) =x²-y²/x²+y² ii) f(x,y) =x³-y³/x²+y² iii) f(x,y) =xy/|x|+|y| iv) f(x,y) =1-√(1-x²)/x²+ xy+y² v) f(x,y) =y³x/y^6+x² im having problems finding the limits especially iii)...