MVC SHOW ALL WORK !! Calculator allowed. Quiz #3 NAME: 1. (8 pts) Let f ( x, y) ( xy 2 3x)3 a. Find f x ( x, y ), f y ( x, y ), and f xy ( x, y ) b. Evaluate f (1, 2) . c. Find the equation of the tangent plane to the graph of f at (1, 2) 2. (8 pts) Evaluate each of the following limits, or show that it does not exist. x2 a. Lim x , y 0,0 x 2 y 2 b. MVC Lim x , y 0,0 x3 y x6 y 2 3. x2 4 y 2 if ( x, y) (0,0) (5 pts) Let G( x, y) y ( x 2 y ) . 0 if ( x, y ) (0,0) Determine with explanation if G is continuous at (0,0) . 4. MVC (5 pts) Sketch the graph of z 2 x 2 y 2 1 . 5. (5 pts) Suppose that you have a function f : ( x, y ) (1, 2) (1.05, 2) (1,1.99) 2 with table of values given below: f ( x, y ) 4 4.1 4.01 a. Estimate the values of f x (1,2) and f y (1, 2) . b. Give an approximation for the tangent plane to the graph of f at (1,2). MVC 6. 2 1 2 if ( x, y ) (0,0) x y sin 2 2 (3 pts) Let f ( x, y ) x y 0 if ( x, y ) (0,0) a. Determine f x (0,0) or show that it does not exist. b. is f x continuous at (0,0)? Explain/show work. c. Determine whether f is differentiable at (0,0) . Again, Explain/show work. MVC