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Describe the Taylor’s theorem for functions of two variables Jacobeans.
Evaluate ]dxdy )x y(dzdx )y z(dydz )x z([ S ∫∫ + + + + + where S: x2 +y2 +z2 = 1
Find volume of the region bounded by the first octant section cut from the region inside the cylinder x2 +y2 =1 and by the planes y=0, z=0, x=y.
In usual notations prove that, = ∇ ∫∫∫ R f dv 2 ∂ ∫∫ ∂ S dA.
In usual notations prove that, = ∇ ∫∫∫ R f dv 2 ∂ ∫∫ ∂ S dA
Evaluate ∫ ∫ 1 0 2 2 2 0 x y dxdy π .
Check whether the line integral ∫ + + (1,2,3) (2,0,0) (xdx ydy zdz) is independent of path or not.
Verify Stoke's theorem for v y i x j 3 3 and surface S: the circular disk− = x 2 +y2 1, z=0.≤
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