Please help

1. (2 points) Consider the function Is f differentiable at (0,0)? f(x,y) = F+7 (x,y) # (0,0) 0, (x, y) = (0,0) . yes . no (a) Use a computer to draw a contour diagram for f. Which . it is not possible to tell of the following is the contour diagram? (e) Find the partial derivative f, at (0,0) by calculating it di- rectly with a limit: . figure I fy = lim =(f (--)-/(--))=. . figure 2 . figure 3 Do the partial derivatives f and f, exist and are they contin- . figure 4 uous at (0,0)? (Hint: to test continuity, you may want to use a similar calculation as you used to test the continuity of f) . yes . no . it is not possible to tell . they exist but are not continuous lem.) (Be sure that you can justify all of your answers in this prob- [?/yeso] (b) Is f differentiable at all points (x,y) * (0,0)? (c) Calculate the partial derivatives of f for (x,y) # (0,0): fx =. Do the partial derivatives fx and fy exist and are they continuous at all points (x, y) # (0,0)? . they don't exist at at least one point . they exist but aren't continuous at at least one point . . they exist and are continuous at all points (d) A first test for whether f is differentiable at (0,0) is to see if it is continuous there. Calculate each of the following limits to determine if f is continuous at (0,0): lim f(0, h) =_ 4-+0" lim f(h,0) = lim f (h, h) = (In each case, enter DNE if the limit does not exist.) Is f continuous at (0,0)? .no . it is not possible to tell