9 draw the level surfaces of f x y p x 2 2 y 1 2 and

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9. Draw the level surfaces of f ( x, y ) = p ( x - 2) 2 + ( y + 1) 2 and then describe the graph of this function.what is the domain of this function?
10. Draw a contour map of the function f ( x, y ) = ye - x showing several level curves.
11. State Clairaut’s Theorem.
12. True or False (and justify your answer): Let f ( x, y ) be a real-valued function. (a) If f x ( x, y ) and f y ( x, y ) exist for all x and y , then f ( x, y ) is continuous.
(b) If f x ( x, y ) and f y ( x, y ) exist for all x and y and both are continuous functions then f ( x, y ) is continuous. Page 5

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