Let C be the curve with parametrization 7 (t) = 8sin(t) 7 - 8cos(t)j + (15t-10)...
(7.5 points) Let C be the oriented closed space curve traced out by the parametrization r(t) = (cost, sint, sin 2t), 0<t<27 and let v be the vector field in space defined by v(x, y, z) = (et - yº, ey + r), e) (a) Show that C lies on the cylinder x2 + y2 = 1 and the surface z = 2cy. (b) This implies that C can be seen as the boundary of the surface S which is...
→ (1 point) Let Vf-6xe-r sin(5y) +1 5e* cos(Sy) j. Find the change inf between (0,0) and (1, n/2) in two ways. (a) First, find the change by computing the line integral c Vf di, where C is a curve connecting (0,0) and (1, π/2) The simplest curve is the line segment joining these points. Parameterize it: with 0 t 1, K) = dt Note that this isn't a very pleasant integral to evaluate by hand (though we could easily...
Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) , Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) ,
(1 point) Let Vf =-8xe-r sin(5y) 20e-x. cos(Sy) j. Find the change inf between (0,0) and (1, π/2) in two ways vf . dr, where C is a curve connecting (0,0) and (1.d2). (a) First, find the change by computing the line integral The simplest curve is the line segment joining these points. Parameterize it: with 03t s 1, r(t)- so that Icvf . di- Note that this isn't a very pleasant integral to evaluate by hand (though we could...
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.
Multivariable Calculus Image Provided Let C be an oriented curve in R3; f = f(x,y,z) a function and F a vector field. Which of the following is true? The Answer Key (without solution) is telling me the answer is D.... I really beg you.. could you please explain the reasons behind why your answer(s) are true and others are false? While exam is soon, I am really having hard time understanding the concept--fundamentals behind it. I will promise to sincerely...
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t<2n. (a) [5 pts] Show that this curve C lies on the surface S defined by z = 2.cy. F. dr (b) (20 pts] By using Stokes' Theorem, evaluate the line integral| " where F(t,y,z) = (y2 + cos z)i + (sin y+z)j + tk
Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t< 27. (a) (5 pts] Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts] By using Stokes' Theorem, evaluate the line integral F. dr C where F(x, y, z) = (y2 + cos x)i + (sin y +22)j + xk
(4) Evaluate the line integral F dr where C is the epicycloid with parametrization given by r(t) 5 cos t - gradient of the function f(x, y) = 3 sin(ry) + cos(y2) cos 5t and y(t) = 5 sin t - sin 5t for 0 < t < 2« and F is the (5) EvaluateF dr where F(x, y) with counterclockwise orientation (2y, xy2and C is the ellipse 4r2 9y2 36 _ F dr where F(r, y) = (x2 -...
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t<2n. (a) [5 pts] Show that this curve C lies on the surface S defined by z = 2.cy. (b) [20 pts] By using Stokes’ Theorem, evaluate the line integral| vi F. dr where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk