# The tangent line to a smooth curve

The tangent line to a smooth curve r(t) = f(t)i + g(t)j + h(t)k at t= to is the line that passes through the point (f(t):9(60) h(t)) parallel to v(to the curve’s velocity vector at ty. Find the parametric equations for the line that is tangent to the given curve at the given parameter value t = to TC r(t) = ( sin t)i + (cost)j + ( sin 61)k, to = 2 x= (Type an exact answer, using radicals as needed.) y = (Type an exact answer, using radicals as needed.) Z= (Type an exact answer, using radicals as needed.) Integrate f(x,y,z) = (x + y + z)/ (x2 + y2 + z2) over the path r(t) =ti + 2t j + 3t k, 00, y> 0. b. the maximum value of xy, subject to the constraint x + y = 16. The minimum value of x +y is y a (Simplify your answer.) The maximum value of xy is (Simplify your answer.) 7 Enter your answer in each of the answer boxes. Use the method of Lagrange multipliers to find a. the minimum value of x + y, subject to the constraints xy = 16, x>0, y>0. b. the maximum value of xy, subject to the constraint x + y = 16. The minimum value of x +y is 17 (Simplify your answer.) The maximum value of xy is (Simplify your answer.)

Purchase answer to see full attachment