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- 7. Find the length of one complete graph of the hypocycloid given by r(t)=D(cos't,sin't) for 011. Let F(x, y, z) = cos³ t sin5 t yz XZ xy and let P represent the path that follows the from (1, 0, 1) to (0, 1, 0), and then goes in a straight path r = line to the point (1,2,3). Find pF. dr.Show that the path given by r(t) = (cos t,cos(2t), sint) intersects the xy-plane infinitely many times, but the underlying space curve intersects the xy-plane only twice.1. Evaluate (2,5) (3x+y)dx+(2y-x)dy (0,1) (i) along the straight lines from (0, 1) to (2, 1) and then from (2, 1) to (2,5), and (ii) along the parabola y = x² + 1. Don't use any Al tool show ur answer in pe n and paper then takeD,E,F1) Let z = 2+i be a point on a curve C. The direction of the tangent vector to C at z = 2+i is rotated through an angle θ under the action of the transformation f(z) =36z2+12z on C. Then the value of tan θ is. 2) The image of the line y = 5x under the mapping w = z2 is a straight line L. Then the slope of L is 3)A non-zero fixed point of the mapping w = 14z/(11z+2) is 4) If u(x,y) = 2x+3xy+c is the real part of an analytic function f(z), then the derivative of f at 5i, f'(5i) =2. In the following cases, express the f(t) as a single sinusoid: a. f(t) = cos wat - √3 sin wat b. f(t)=-3 cos wat + 4 sin watCompute the Jacobian at the indicated point. G(r.1) = (r sin (1), r- cos (f)), (r.t) = (5,-) (Express numbers in exact form. Use symbolic notation and fractions where needed.) Jac(G) (5,) =01 (h) B A Which of the space curves above describes the vector-valued function: r(t) = (cos³ t, sin³ t, sin 2t)? Enter the number of the correct figure using one of the numerical labels 1 through