1) Find the largest possible domain and corresponding range of the function f (x, y) = V9 -22 -yz. Determine the equation of the level curves f(x, y) = c, together with the possible values of c. 2) latch each function with the appropriate graphs below (1) f(x, y) = 1+2+2. (2) f(x, y) = sin(x) . sin(y) , (3) f(x, y) = y2 -2, (4) f(x, y) = 4-22 (a) (b) (c ) (d) Explain your answer. 3) Let f : R2 \\ {(0, 0) T} - R be given by f (x, y) = 202 - 212 2 2 +2 Show that lim (x,y) -(0,0) f (x, y) does not exist by computing the limit along the positive x-axis and the positive y-axis.4) Information: (b) "Linear approximation" refers to the "tangent plane", (b) the concept of a directional derivative will be topic of the lecture on March 15. Find of and dy f(x, y) = tan(x - 2y) . 5 ) of for Find ayox f(2, y) = x. ey . 6) Find the linear approximation of f(x, y) = tan(2 . x - 3 . y2) at (0, 0) and use it to approximate f (0.03, 0.05). Compare the approximation with the exact value f (0.03, 0.05). 7) Let f(x, y) = Vx2 + y2 with x(t) = t and y(t) = sint. Find the derivative w'(?) for w ( t) = f(x(t), y (t) ) . 8) Find the gradient of f(x, y) = Vx3 - 3. x.y