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6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) - (sin t, cos t, sin 2t), 0 s t s 27. (Hint: Observe that C lies on the surface z - 2xy.) F dr- 6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) -...
Show that cos e+sin e) sec2 e+2tan 2 cos2 e (12) (a) Hence find all values of 0, where 0<0< 2T, which satisfy the equation sec20+ 2 tan 0 (b) =2(2 + tan e) (cos e+sin e)
F(x, y) = (3x2 + sin y)i + (x cos y + 2 sin y)j. Question 1 (8 points) Find a potential function for the vector field F. Enter this function in the answer box. - Format B I U , . A X Question 2 (6 points) Use the potential function you found in problem 1 to evaluate F. dr, where Cis given by r(t) = (2-t)i + (ret/2), 0 st < 1.
(5) The image of the parametrization Φ(u, u) = (a . sin(u) . cos(u), b . sin(u) . sin(e), c . cos(u)) sin(u sin() cosu with b < a, 0 r, 0 2π parametrizes an ellipsoid. u u a) Show that all the points in the image of Φ satisfy the Cartesian equation of an ellipsoid E b) Show that the image surface is regular at all points. c Write out the integral for its surface area A(E). (Do not...
Entered Answer Preview Result [e^(-2*1)]*[8*cos((9/5)*1)-14*sin((9/5)*t)] - * (cos(.) – 14 sin(6-)) incorrect The answer above is NOT correct. (1 point) Find y as a function of t if 25y" + 100y + 181y = 0, y(1) = 8, y'(1) = 2. y= e^(-2*t) * (8*cos(9/5*t) -14*sin(9/5*t))
Question 1. Let y : R -> R' be the parametrised curve 8 (t)= 1+ sin t Cost 5 Cos (a) (2 marks) Show that y is unit speed (7 marks) Find, at each point on the curve, the principal tangent T, principal normal (b) N, binormal B, curvature K, and torsion 7. (c) (3 marks) Show directly that T, N, B satisfy the Frenet-Serret frame equations (d) (3 marks) Show that the image of y lies in a plane...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
4.Consider the curve described by the parametric equations x= sin(t)=cos2(t) ,y= sec(t). Verify that all points on this curve satisfy the equation x^2+y^2=y^4
2 + COS- 2.ry dy d 1+y2 = y(y + sin x), 7(0) = 1. 3. [2cy cos(x+y) - sin x) dx + x2 cos (+²y) dy = 0. 4. Determine the values of the constants r and s such that (x,y) = x'y is an Integrating Factor for the following DE. (2y + 4x^y)dr + (4.6y +32)dy = 0. 2. C = -1 You need to find the solution in implicit form. 3. y = arcsin (C-cos) 4. r=...
Please solve this question The image of the parametrization Ф(u, u)-(a . sin(u) . cos(v), b . sin(u) . sin(v), c . cos(u)) with óくa, 0 < u < π, 0 < v < 2π parametrizes an ellipsoid. a) Show that all the points in the image of Ф satisfy the Cartesian equation of an ellipsoid E 2 b) Show that the image surface is regular at all points c) Write out the integral for its surface area A(E), (Do...