MATH 126 Midterm: MATH 126 UW Midterm 2 Fall 09taggartExIIans
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Math 126 exam ii hints and answers. 3. (a) (7 points) hint: r (2) = 4, 2, 6 and r (2) = 2, 1, 1 . 56 (b) (3 points) answer: 4(x 4) 2(y + 5) + 6(z 10) = 0 or 4x 2y + 6z = 86 or. 2x y + 3z = 43 (a) (4 points) hint: fy(x, y) = e xy(sin y + x cos y) Answer: fyx(x, y) = e xy(cos y y sin y xy cos y) (b) (4 points) hint: fx(x, y) = ye xy cos y. The tangent plane is the plane with normal vector 0, , 1 that contains the point ( , 0, f ( , 0)) = ( , 0, 1). Answer: there is a saddle point at (3, 0) and a local minimum at (2, 1). (b) (2 points) hint: g(x, 0) = 1. 2 x2 3x, a quadratic whose graph is a parabola that opens up.
