Let F=<-yz, xz, xy >. •[ f, cu S is the part of the paraboloid z = 10 - x² - y² that lies above the plane z = 9, oriented upwards Use Stokes' Theorem to evaluate curlFdS, where

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Q: 2. (b) Q 3 p sin фа, + p'zag +z cos ф a,

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Q: Your friends correctly calculate the gradient vector for f(x, y)=x²+y at the point (2,-3) as…

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Q: Use Stokes' theorem to evaluate I = ff, Vx F. ds where F = (2²,-3xy, x³y³) and S is the part of z =…

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Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: F · dr  where F  =  (x + 5z) i  +  (7x + y) j  +  (2y − z) k   and C is the curve of intersection of…

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Q: Let f ={ (-6,4),(-5,3),(4,-6),(3,-5),(1,5),(2,6),(-3,5),(-8,2),(6,4)}  g=…

A: It is known that f-gx=f(x)-g(x) and f·gx=f(x)·g(x). The sets are provided as:…

Q: Consider the planes P₁: 3x+y-2zm 7 and P₂ : x+2y+z=4. Give a parametrization for the line of…

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Q: Verify Stoke's Theorem. F=, C'is the boundary of the paraboloid z = x² + y² lying pelow z = 1 plane.…

A: To verify Stoke's theorem for the below function. F=y,−xz,xz2

Q: Use Stokes' Theorem to evaluate F• dr where C is oriented counterclockwise as viewed from above.…

A: Here use the stokes theorem to find the integral of the function.  And given that the function…

Q: Use Stokes' Theorem to evaluate curlF · dS, where

A: Let, F→=xyz , xy , x2yz. Stokes theorem states that ," Where C is the boundary of surface oriented…

Q: Let F = . Use Stokes' Theorem to evaluate F. dr, where C is the triangle with vertices (7,0,0),…

A: Given that, F→=5x+y2, 2y+z2, 8z+x2 And vertices of the triangle are, 7,0,0, 0,7,0, 0,0,7. To find…

Q: F(x, y, z) = yzi + 8xzj + exyk, C is the circle x² + y² = 1, z = 4.

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Q: Let F = Use Stokes' Theorem to evaluate с شرح = F. dr, where C is the curve of intersection of the…

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