MATH 126 Midterm: MATH 126 UW Midterm 2 Spring 14perkinsExIIans
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Evaluate the following double integrals. (a) (8 points) 1 + xy da, r = [0, 1] [0, 2] 1 ln(1 + 2x) dx dx (u = ln(1 + 2x), dv = dx) dx. = ln 3 [x ln 3. Zzd xy2 da, d is the triangle with vertices (0, 0), (0, 2) and (1, 2). Let f (x, y) = x2 y2 + 4 ln(xy). Find all points on the surface where the tangent. 2nd midterm solutions (9 points) plane is parallel to the plane 6x = 2y + z. The normal vector to 6x = 2y + z is h6, 2, 1i. The normal vector to the tangent plane to z = f (x, y) at hfx(x, y), fy(x, y), 1i. Thus we need to solve the equations fx(x, y) = 6 and fy(x, y) = 2 for x and y. fx(x, y) = 2x + and fy(x, y) = 2y + the point (x, y) is.
