MATH 599 Final: MATH 5B UCSB 5B Fall 06 5bFinalReview
Document Summary
Fall 2006: suppose u = cos x + y and v = sin y x. (u,v) is simply the inverse of the jacobian matrix cos y (cid:19). The determinant of this matrix is sin x cos y + 1, and. 1 sin x cos y is the upper left entry of this jacobian, while is the lower right entry. (cid:18) y. Let f (x, y, z) = x2 + yz 1, so that we must check that f (cos t sin t, 2 sin t, cos t) = 0. We have f (cos t sin t, 2 sin t, cos t) = (cos t sin t)2 + The coordinates of the point on c when t = /4 are (x( /4), y( /4), z( /4)) = (0, 2, 2/2). Thus the parametric equation of the tangent line is x(t) = t 2 y(t) = 2 + t 2 z(t) = 2/2 t 2/2.
