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Limits and Continuity Reading assignment: 2.1, 2.2 Recommended problems: 2.1: 1, 3, 5, 7, 14, 19, 21, 27, 28, 31, 32, 33, 34, 36 – 42 2.2: 9, 11, 13, 15, 17, 22, 24 – 27, 28, 29, 31, 33, 41, 46. 48 For each function below, either provide a value for f(0, 0) that will make the function continuous or explain why no such value exists. Justify your results. 1) f ( x, y ) 2) f ( x, y) x x y2 2 x3 x 2 xy 2 y 2 x2 y 2 3) f ( x, y ) xy x y 4) Carefully sketch some of the level curves of g ( x, y) y 2 x 2 . Attempt to sketch the surface. Keeping x and y in a range of [ 3,3] should be fine. y 3 x -3 -3 3 5) Find an equation for the tangent plane to the surface z x 2 y 2 at an arbitrary point (a, b, c) on the surface. Sketch. 6) Evaluate the following limit, or show that the limit does not exist. a. b. lim ( x , y ) (0,0) sin( xy ) x2 y 2 Lim [( x 2 y 2 ) Ln( x2 y2)] (x , y ) (0,0)