MATH 126 Midterm: MATH 126 UW Midterm 2 Winter 11bekyelExIIans
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Math 126, sections a and b, winter 2011, solutions to midterm ii: answer the following. (a) (4 points) below is a graph of the surface z = f (x, y). | < 1/2, 1, 1 > |3 r ( /3) = h1/2, 1, 1i r ( /3) = d . 27 (c) (3 points) the vector function r(t) has the graph below. As t increase, it is traced in the direction of increasing x. The speed of the particle decreases as it gets further away from the origin. The point (3. 5, 5, 0) is on the curve and corresponds to the value t = t0. Sketch the vectors r(t0), r (t0), r (t0) on the rst picture and the vectors t(t0), Approximate the curvature from the graph explaining your reasoning. The vectors r (t0) and t(t0) have to be tangent to the curve, point in the direction of increasing x, and t(t0) must have length 1.
