ENGR 251 Midterm: ENGR 251 Midterm 2007 Winter
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Find the normal component of the acceleration an for a particle that moves as described by the vector-valued function. Find the work done by the force eld ~f (x, y) = y2i xyj along the curve. ~r(t) = (cid:10)2t, t2(cid:11) during the time from t = 0sec to t = 2sec. Recall that given any scalar function f (x, y, z) we have the identity curl(grad(f )) = 0 . Compute the curl of the vector eld below and explain in words why it is not the gradient of any function. ~f (x, y, z) = (cid:10)y2, 2xy, x(cid:11) Find an equation for the tangent plane to the following surface at the indicated point x3y z2 + xyz = 5 , ( 1, 2, 1) Nd the equation of the tangent line at the point ( , 2, 0). One of the following integrals is independent of the path; nd which one and evaluate it ( ,2)
