MA 227 Midterm: 3-12s-test2
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Please always explain your answer, at least by including your calcula- tions. A right answer without calculation brings you no credit: evaluate the double integral where d is bounded by y = 2x and y = x2/2. Y px3 + 1dxdy by reversing the order of integration. 2: find the limit, if exists, or show that the limit does not exist. lim (x,y) (0,0) 12 points: find frrr and fsss for f (r, s, t) = ln(r2s4t6). 12 points: use di erentials to estimate the amount of thin in a closed thin can with diameter. 10 cm and height 16 cm if the thin is 0. 02 cm thick. 3: use implicit di erentiation to nd z/ x and z/ y if x2 + y2 + z2 = cos(x + y + z). 4: let z = x2 when u = 2, v = 1, w = 0. 2xy3, x = uv + w3, y = u + ew.
