MATH 215 Midterm: exam1w16
Document Summary
Winter 2016, math 215 calculus iii, exam 1. Suppose that the rate of change of f at the point. P (1, 2) in the direction from p to q(0, 1) is 2. D~uf (1, 2) = 1 where ~u = 1. Find the partial derivatives fx and fy at p (1, 2). 2: (5 points) consider the function f (x, y, z) = x2 + y2/2 + 2z2 + 2xz. Find all points on the level surface f (x, y, z) = 4 at which the tangent plane is parallel to the xy-plane: (5 points. No partial points) find a parametric equation of the curve of the intersection of the paraboloid z = 4x2 + y2 and the cylinder x = y2: (5 points) consider the vector ~v = h3, 1, 5i. ~v = ~a + ~b where the vector ~a is parallel to the line ~r(t) = h 3, 1, 4i + th1, 2, 3i and the vector.
