8xz Calculate line integral F. dr of conservative vector field F(x, y, z) = i Y A from (-4, 2, 1) to (-4,-8,6). Enter an exact answer. 4x² z y² j+ 4.x² Y -k, where A is a path
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- Consider the vector field v(x)=(y/(x^2+y^2))i − (x/(x^2+y^2)) j + 4k. Calculate ∫Cv dr, where C is the straight line from (1,0,1)to (0,1,2).Compute the flux of the vector field (4, - y²), out of the rectangle with vertices (0,0), (2,0), (2,6), and (0,6).Given the vector field v=⟨0,2xz+3y^2,4yz^2 ⟩. Find the line integral of the path from (0,0) to (0,1). Please show full solution legibly. Thank you!!
- Find the k component of (curl F) for the following vector field on the plane F=(xe^2y)i + (8ye^x)jDetermine if the scalar vector field is Lipschitz Continous on the indicated domain. f(t,x) = SiN (Ex), _√2 = R, I= R XConsider the following system dx = x(1-x-y) dy = y(0.5-0.25-0.75x) 1. Use XPPAUT dt di to plot nullclines, determine stability, and draw vector fields with \epsi 0.0001 (submit printed figures ).