Please help for question (e), my answer input is lim (1/h)( f(h,0)-f(0,0))=0, but the answer is found to be wrong on the first term f(h,0) and say it should be a number instead of unknown h. Would you please help? Thanks.

1. (2 points) Consider the function Is f differentiable at (0,0)? (x,y) # (0,0) VCS (x,y) = (0,0) .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 =((--)-1(- -))= - figure 2 . figure 3 Do the partial derivatives f, and fy exist and are they contin- . figure 4 uous at (0,0)? (Hint: to rest continuity you may want to use a similar calculation as you used to test the continuity of f) (b) Is f differentiable at all points (x, y) * (0,0)? [?/yeso] (c) Calculate the partial derivatives of f for (x,y) * (0,0): / =. fy=- 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 . 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 /(0,h) = lim /(h,0) = 4 +0 lim f(h,h) = (In each case, enter DNE if the limit does not exist.) Is f continuous at (0,0)? ? yes .no . it is not possible to tell