MATH 21A Midterm: MATH 21A Harvard 21a Spring 09Midterm2 Practice3
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The region includes the boundary of the triangle. 3 the contour plot of the function f (x, y) is given in the gure below. 4 a moth"s position at time t seconds is given by the position vector r(t) = hcos( t), t sin( t), 10i (for t 0). Suppose the temperature at any point in space is given in degrees fahrenheit by. T (x, y, z) = 2xz + y2 + z3 + 40. 5 let f (x, y) = g(x2y) where g is a continuous function of one variable with continuous rst and second derivatives. Calculate fxy(2, 2) + fyx(2, 2) if you also know that g (8) = 3 and g (8) = 1. 2 (c) find a unit vector w such that dwf (1, 1) = 0. 7 captain kurt of the starship interprize has steered his starship toward a wormhole in space.
