Find a function f(x, y, z) such that Vf is the constant vector (4, 8, 2). (Use symbolic notation and fractions where needed. Use C for the constant of integration.) f(x, y, z) =
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- Integrate f(x, y) = (x + y + 1)- 2 over the triangle with vertices (0, 0), (4 , 0), and (0, 8).integrate ƒ over the given curve. ƒ(x, y) = x3>y, C: y = x2/2, 0 <=x<= 2.True or False and explain1- For any two non parallel and non orthogonal vectors a and b with angle θ between them, it holds that cosθ(a.b) = sinθ(axb). 2- Ifr(t)=⟨−4cos(2t),3sin(3t),ln(2t)⟩,then the ∫r(t)dt is equal to⟨−2sin(2t),−cos(3t),tlnt−t⟩+C,where C is a vector constant of integration.
- A mass m moves along the x-axis subject to an attractive force given by 19mx/2 and a retarding force given by , where x is its distance from the origin and is a constant. A driving force given by , where A is a constant, is applied to the particle along the x-axis. D)what is the Q value?Find all solutions to r'(t) = v with initial condition r(1) = w, where v and w are constant vectors in R^3.Find the gradient, ∇f(x,y,z), of f(x,y,z)=xy/z. Express your answer using standard unit vector notation.