Let f(x, y) = 10 - x^2 - 3y^2. (a) The graph of f is a surface in R^3. Name this surface. (b) Find lim_(x, y) rightarrow (2, 1) f(x, y). (c) Find f_x(2, 1) and f_y (2, 1). (d) Find an equation for the plane tangent to the graph of f at (2, 1, 3), expressing your answer in the form Ax + By + Cz = D for some constants A, B, C, D.
Show transcribed image text Let f(x, y) = 10 - x^2 - 3y^2. (a) The graph of f is a surface in R^3. Name this surface. (b) Find lim_(x, y) rightarrow (2, 1) f(x, y). (c) Find f_x(2, 1) and f_y (2, 1). (d) Find an equation for the plane tangent to the graph of f at (2, 1, 3), expressing your answer in the form Ax + By + Cz = D for some constants A, B, C, D.