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

Q: Let S be the surface defined by the vector function R(u, v) = (2e" sin v, 2e" cos v, u²+u), where u…

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Q: Let L be the line segment with endpoints at (1,2,3) and (-1,1,4). A light source at is at the point…

A: We will find shadow of given points on the plane given and then find parametric equation of the line…

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: Let S be the surface defined by the vector function R(u, v) = (u cos v, u – v, u sin v) with u ER…

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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: An equation of the tangent plane to the surface z = 4xy² + 3x²y² at the point (1, 1, 7) is: Select…

A: z= 4xy2+3x2y2F(x,y,z) =…

Q: Use Stokes's theorem to evaluate fF.dR or ff(V x F) ndo, whichever appears easier: F = xyi-yzj +…

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Q: Evaluate F.dS, where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 3, 0 < v < T…

A: Given that, F¯=y,-x,z5 and ru,v=u cos v, u sin v, v where 0≤u≤3 and 0≤v≤π. Find ru×rv as follows.…

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: 3) Evaluate, to the nearest hundredth, 11. (V x F) dS where F = and S = {(x, y, z)| 2² − 1 = 3x² +…

A: Here we will use Stokes theorem  According to stokes theorem  ∫∫S∇×F.dS=∫CF.dr C is the  boundary…

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: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: kpression for "12 times x."

A: Times means multiplication. Sometimes it is denoted by dot.

Q: a) Find the unit tangent vector 7(1), unit normal vector Ñ(t), and unit binormal vector B(t) to the…

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Q: a. Sketch the surface x2 - y2 + z2 = 4. b. Find a vector normal to the surface at (2, -3, 3). Add…

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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: 2)Use Stokes' Theorem to evaluate [F.dr where E2xyi, y² j‡ 2xzk and Sis the first octant с surface…

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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: Let S be the surface obtained by revolving the plane curve 2x = /9 – y² about the y-axis.

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Q: :) Use Stokes' theorem to evaluate RF dr where C F = z?i + yj + xk and C is the triangle with…

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

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Q: Let S be the surface defined by the vector function R(u, v) = (u cos v, u – v, u sin v) with u eR…

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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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Q: Use Stokes' Theorem to find m # 0 satisfying F · dr = -5, whereF(r,y, z) = (3yx² + z³, y², 4yx²) e C…

A: Given: