a)
Kind regards
Let f(x,y) = if (x,y) doesnt equal (0,0) and
0 if x = y = 0
a) Find (0,0) and (0,0)
b) Is f continuous at (0,0)?
c) Is f differentiable at (0,0)? Explain.
Attempt:
a) (0,0) and (0,0) both = 0
b) No since f(x,y) = 0 (if x = y = 0) and (if (x,y) doesnt equal (0,0)
c) It isnt differentiable at (0,0) similar reasoning as b
It would be better if you showed how you got these- then we could comment. is certainly NOT 0. Since f(0, 0)= 0, the partial derivative with respect to x is give by
What? You appear to be saying that any non-constant function is not continuous!b) No since f(x,y) = 0 (if x = y = 0) and (if (x,y) doesnt equal (0,0)
What is the limit of f as (x, y) goes to (0, 0)?
What reasoning? All you did was repeat the definition of the function!c) It isnt differentiable at (0,0) similar reasoning as b
what is the definition of "differentiable" for a function of two variables?