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(b) Compute the upper bound of
dz where C2 is the top half of circle with radius
- 1
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- Use Green’s theorem to evaluate the line integral 2x2y dx + 6x3 dy, where C is the circle x2+y2 = 4, traversed counterclockwise.What is the shortest distance from the surface xy +12x +z^2 =144 to the origin?E is the region contained between and on the sphere of radius 2 and the sphere of radius 5 centered at the origin.
- Let C denote the circle of radius 1 in R2centered at the origin, oriented counterclockwise.for which F(x, y) = <1,y> Compute F*drShow that the hyperbolic spiral r = 1/θ (θ> 0) has a horizontal asymptote at y = 1byshowing that y→1and x→+∞ as θ→0 +. Confirm this result by generating the spiral with a graphing utility.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
- Let CR be the circle of radius R centered at the origin. Use Green's Theorem to find the value of R that maximizes J y3 dx + x dy.Use Green's Theorem to evaluate the line integral along the given positively oriented curve. ∫C 7y3dx - 7x3dy C is the circle x2 + y2 = 4Calculate the double integral ∬R(x2+y2)dxdy in the circle x2+y2=2x.