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QUESTION 1 Let f(x, y)=2xy +2. Find and sketch the level curves f(x, y) = 0, f(x, y) = 2, f(x, y) = 4,

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QUESTION 1 Let f(x, y)=2xy +2. Find and sketch the level curves f(x, y) = 0, f(x, y) = 2, f(x, y) = 4, and f(x, y) = 6. You may draw all of them in the same plane. Let f(x,y) = 16 x 4y. QUESTION 2 (a). Find and sketch the domain of this function. (b). Find and sketch the level curves f(x, y) = 0, f(x, y) = 2, and f(x, y) = 4. You may draw all of them in the same plane. (c). Find the range of this function. Let f(x,y) = (a). Find the domain of f. QUESTION 3 (b). Find and sketch the level curves of f(x, y) = 1, f(x, y) = 0, and f(x, y) = 1. You may draw all of them in the same plane. Let f(x, y) = QUESTION 4 (a). Find the domain of this function. (b). Find and sketch the level curves f(x,y) = 1, f(x,y) = 0, f(x,y) = 1, and f(x,y) = 2. You may draw all of them in the same plane. Let f(x,y) = ln(x + y). QUESTION 5 (a). Find the domain of this function. (b). Find and sketch the level curves f(x,y) = -2, f(x,y) = 0, and f(x, y) = 2. You may draw all of them in the same plane. QUESTION 6 Compute the following limit, or show that it doesn't exist. Make sure to justify your answer in full. lim (x,y)(0,0) 2+ y 1 QUESTION 7 Compute the following limit, or show that it doesn't exist. Make sure to justify your answer in full. lim (x,y)(0,0) x-2xy + y x + y QUESTION 8 Compute the following limit, or show that it doesn't exist. Make sure to justify your answer in full. lim y' sin(x) (x,y)(0,0)+31 Let (a). Find the domain of f. QUESTION 9 f(x,y) == (b). Determine whether the values 0, 1, and -1 are in the range of f. Justify your answer. (c). Find and sketch the level curves f(x, y) = and f(x,y) =. You may draw all of them in the same plane. (d). Compute the following limit, or show that it doesn't exist. Justify your answer. lim (x,y)(0,0) f(x,y) (e). (Optional; extra credit, 5 points.) Find the range of f. Justify your answer.

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