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Unformatted text preview: x, y ) = (1 , 1) to (0 . 95 , . 95) by assuming that the hiker moves along this tangent plane. What is the error resulting from this approximation? b) When the hiker is at the point (1 , 1 , 995), in what direction should she move in order to ascend as rapidly as possible? c) If she continues to move on a path of steepest ascent, show that the projection of this path on the xy-plane is y = x 3 / 2 . Problem 2. (Tues. 8pts: 4 + 4) a) Find the tangent vector at the point (1 , 1 , 2) to the curve of intersection of the surfaces z = x 2 + y 2 and z = x + y . b) Generalize this result to nd an expression for the tangent vector of the curve of intersection of any two surfaces z = f ( x, y ) and z = g ( x, y ) at a point of intersection P = ( x , y , z )....
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- Winter '10