let f : R^2 -> R be defined as:
f = x^3 / (x^2 + y^2) if (x,y) =/= 0
and 0 if (x,y) = 0.
let g be any curve in R^2 that passes through the origin. then show that f o g is differentiable while f itself is not. so i have that g: R -> R^2 and using the definition of the limit i have lim (h->0) [f(g(h)) - f(g(0)) - mh]/h which we want to show should = 0. i am evaluating the derivative at 0 because at any other point where (x,y) =/= 0 then f is differentiable so the only trouble spot comes from (x,y) = 0. however i am stuck since i don't know anything about g, just that its a curve that passes through the origin which does not help me figure out what f(g(h)) could be. any help is greatly appreciated. thanks.