Please solve these questions in the picture:

In which points the function f xsexy f (x, y) = x2fey; in those points, where this term is well-defined and when(x, y) * (0, 0) 0; (x, y) = (0,0) is continuous? In which points the function is defined? If the function is continuous in the point (0, 0), prove it by using the definition of continuity at (0, 0). In this case the limit value at (0, 0) has to be proved by using the definition of the limit value. Calculate the partial derivative ay of (0, 0) and of (0, 0) by using the defini- tion of the partial derivative if it exists.Determine the Taylor polynomial of degree 2 for the function f (1:, y) = sin(a:y) near the point (1,1) (i.e. the polynomial has the same value as the function f at (1,1)). Determine and classify the local maximum and minimum points of the function f(x, y) = x sin(y) in the set that defines the condition x2 ty-