Compute e3z dz , Jy (z – 1)2(z+ i) where +y is any simple closed curve oriented counterclockwise whose interior contains the points z = 1 and z = -i.
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A: Total derivative
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A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…
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Q: b) Show that the force field F(r, y, z) = 3x zi+ 2y ln z j+ is independent of path and find its…
A: F(x,y,z)=3x2zi +2ylnzj+(y2/z +x3)k r(t) =ti +tj+t2k F(t ) =3t4i +4tlnt j +(1+t3)k dr = dt i +dt j…
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Q: 1. Calculate the work done when a force F = 3xyî – y?j moves a particle in the xy-plane from (0,0)…
A: Take dot product along limit of integration and integrate
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Q: Calculate of A= Xzi- 2x*yzj+2yz'K at ( 1,-1,2). the Curl and Divergence
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- Find a parametrisation of the curve of intersection of the surfaces: x^2 + 2y^2 + z^2 = 5 and x^2 + y^2 = 1 which lies in the first octantFind the parametrization of the curve defined by the intersection of the two surfacesy = x^2 − 3z^2 and x^2 + z^2 = 9, where x ≥ 0.Compute ∫C(2x+√y)ds, where Cis the curve from (0,0) to (2,4) along y=x^2.
- A point moves along the curve of intersection of the paraboloid z=x^2+5y^2 and the plane x=3. At what rate is z changing with y when the point is at (3,-1,14)?Find the appropriate parametrization for the given piecewise smooth-curvein R^2, with the implied orientation. The curve C, which goes along the circle of radius 3, from the point(3,0) above the x-axis to the point (-3,0), and then in a straight line along the x-axis back to (3,0).The plane curve C is the part of y = x^4 that begins at the point (−1, 1) and ends at the point(1, 1). Evaluate the line integral
- Find the tangent plane to the surface xz+2x2y +y2z3=11 at the point (2,1,1)A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 4.90 s, it is at point (4.60 m, 5.00 m) with velocity (2.00 m/s)ĵ and acceleration in the positive x direction. At time t2 = 13.6 s, it has velocity (–2.00 m/s)î and acceleration in the positive y direction. What are the x and y coordinates of the center of the circular path? Assume at both times that the particle is on the same orbit.