MATH 226 Midterm: MATH 226 2007 Winter Test 1
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Name: (8 points) compute the following limits or explain why they do not exist. (a) (b) lim (x,y) (0,0) lim (x,y) (0,0) xy x2 + y2 . |y|x. (c) lim (x,y) ( 1,1) x2 + 2xy2 + y4. 1 + y4 (d) lim (x,y) (0,0) sin xy x2 + y2 . Name: (12 points) suppose that a planet moves around the sun in a circular orbit of radius r > 0 with the sun at the center. By kepler"s third law, the period t of the orbit (i. e. , the length of a year on the planet) is given by where is a positive constant. If it does, compute them. (c) does f have any global minima or maxima on {(x, y) r2 | x 0, y 0}. Name: (10 points) let z = f (x, y) and set x = 3s + 2t, y = s + 2t.
