Recent content by minor_embedding

I realize that my question probably sounds pretty idiotic with or without the problem statement. But what I'm confused about is if it's not continuous at the origin, then it can't be differentiable at the origin. So then how is it defined everywhere? Does the second part of the piecewise take...

So 1 is definitely true, but what does it mean to be a well defined partial derivative?

Homework Statement I was given the following function f(x,y) = \begin{cases} \frac{x^2y}{x^4+y^2} & (x,y) \neq 0 \\ 0 & (x,y) = 0 \end{cases} Which of the following are true? (I) f is not continuous at (0, 0). (II) f is differentiable everywhere (III) f as a well defined partial...

Homework Statement We have a set S = {a,b,c,d} and a set X such that X = {##f:S \rightarrow S| ## f is bijective and ## f(x) \neq x## for each ##x \in S##}. What is the order of the set? 2. Attempt at Solution/My Reasoning The order of the set of all bijective functions is simply the 4...