(1 point) Let (u, v) = (7u+ 3v, 5u + 8v). Use the Jacobian to determine...
QUESTION 16 Find the Jacobian 2 (x, y) using x = 7ucosh(8v), y = 7u sinh(8v). a(u, v) OA 448u ов. 392u Ос. 448uv OD. 392v OE 448v
Solve the following relations for x and y, and compute the Jacobian J(u,v). u=x+3y, v = 5x + 4y x=y=0 (Type expressions using u and v as the variables.) Choose the correct Jacobian determinant of T below. a A. J(u, v) = du - 4u + 3v a 11 - 4u+ 3v 11 a O B. J(u,v) = -4u + 3v 11 a (5u-v dy du Mal . (517") i (517) (507°) (-44*34) dic (547) OC. Jusv) = m (...
(1 point) Let u = (-2,-3) and v = (-1,6). Then u+v=< >, u-v=< -3v=< u.V= and || 0 ||
Consider the elliptic paraboloid which is given by (1) = {r(u, v) = (5u cos(u), 5u sin(u), u?)? | >0, v € (-,7]} . Below, we work in the chart (U,r) obtained by taking U = RX0 X (-,7), where the map r:U + R3 is defined in (1). 0 Question 2 (1 mark). Show that the second fundamental form II is given by 10 10 14u2 + 25 ( 0 u =
1 point) Show that Φ(u, u) (Au + 2, u-u, 7u + u) parametrizes the plane 2x -y-z = 4, Then (a) Calculate Tu T,, and n(u, v). þ(D), where D = (u, u) : 0 < u < 9,0 < u < 3. (b) Find the area of S (c) Express f(x, y, z in terms of u and v and evaluate Is f(x, y,z) ds. (a) Tu n(u,v)- T, (b) Area(S)- (c) JIs f(z, y,2) ds- 1 point)...
Let 7u + 6V g(u,v) = 20 Find oʻg(u,v) at the point (u, v) = (-5,3). duðv
1. Let u - (1,1,2), v = (1,2,1), and w (2,1,1) in R. and consider • the parallelogram B = {s(3v) + t-w) 0 <s,t<1, s,te R} spanned/formed by the vectors (3v) and (-w), and • the parallelepiped P = {ru + s(3v) + (-w) 0 <T,,t<1, r, s, t€ R} [10] spanned formed by vectors u. (3v). and (-w) We take the parallelogram B as a base of P. (a) Does the ordered vector triple (v xw, 3v, -w),...
How to get joint pdf with jacobian matrix? Let V = X and U = Xy, then X = V and y = I. The Jacobian is 2 V I+ Let V = X and U = Xy, then X = V and y = I. The Jacobian is 2 V I+
QUESTION 18 Find the Jacobian 2(x,y) using x = 7ucosh(Sv), y = 7usinh(8v). Ə(u, v) ОА 392v OB 448u OC 448v OD 392u ОЕ 448uv
(1 point) 5x2 — 5у, v %3D 4х + Зу, f(u, U) sin u cos v,u = Let z = = and put g(x, y) = (u(x, y), v(x, y). The derivative matrix D(f ° g)(x, y) (Leaving your answer in terms of u, v, x, y ) (1 point) Evaluate d r(g(t)) using the Chain Rule: r() %3D (ё. e*, -9), g(0) 3t 6 = rg() = dt g(u, v, w) and u(r, s), v(r, s), w(r, s). How...