MATH V1207 Final: MATH V1205 Columbia Spring01Final
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Final: may 9, 2001, 9:00 am 12:00 noon. The following nal has 20 problems which are each worth 5 points. Please read the exam carefully and check all your answers. Some of the problems are harder than others, so move on if you get stuck. Circle exactly one answer for each question: name, a hummingbird is hovering at the point (2, 4, 2) and the surrounding temperature is given by the function f (x, y, z) = xyz. Find the rate of change of the temperature as the hummingbird ies in the direction of the vector ~v = h4, 2, 4i: 1/2 b. 1/4 c. 1/6 d. 1 e. 3/2: icecream lls the space below the sphere x2 + y2 + z2 = a2 and above the cone. Find the mass of the icecream using spherical coordinates. z = px2 + y2.