Let CR denote the circle z = Rei (0 ≤ 0≤ 2π). Show that lim R→∞ CR 2-4 (2² + 1) (2³ — 5) dz = 0
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Please help with the following Complex Analysis question.
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- Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?Evaluate ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9 with positive direction using Green's Theorem.Use Green’s theorem to evaluate the line integral 2x2y dx + 6x3 dy, where C is the circle x2+y2 = 4, traversed counterclockwise.
- Let C be the positively oriented circle x2 +y2 =1. Use Green's Theorem to evaluate the line integral ∫C 3ydx+9xdyFind a parametric description for the circle x2+y2-6y=0, oriented clockwise and where t begins at 0. Restrict the domain of t such that one full revolution occurs.Use Green’s Theorem to evaluate the line integral ∫_c (x+ 2y^3)dx + (2x − 3y)dy where C is the positively oriented, simple closed curve given by the circle x^2 + y^2 = 16
- Use Green's Theorem to evaluate the line integral along the given positively oriented curve. ∫C 7y3dx - 7x3dy C is the circle x2 + y2 = 4If the infinite curve y = e−4x, x ≥ 0, is rotated about the x-axis, find the area of the resulting surface.Let C denote the circle of radius 1 in R2centered at the origin, oriented counterclockwise.for which F(x, y) = <1,y> Compute F*dr
- Use Green's Theorem to evaluate the line integral ∫c ( x − y ) dx + ( x + y ) dy where C is the circle x2 + y2 = 9 with positive orientation.Determine a∈R such that ∫CF⋅dr = −2−(3π/4), where F (x, y) = (ay, (x^2 − y)/2) and C is the part of the circle with center at the origin and radius 1, with y≥0, followed by the part of y = x^2−1 of x = −1 a x = 1.Calculate the double integral ∬R(x2+y2)dxdy in the circle x2+y2=2x.