Verify Stokes' theorem for F = z²i – y²j and the curve C is the square in the xz-plane from (0,0, 0) to (0,0, 1) to (1,0, 1) to (1,0,0) back to (0,0,0). This means that you need to evaluate both f F.r dr and ff V × F dS.

Q: Find an equation of the tangent plane to the surface z = -2z² – 2y?- lz 2y+ 3 at the point (5, 1,…

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Q: Find the Directional derivative of the function f(x,y,z) = /x² + y² + z² from point (1,2, –2) in the…

A: The objective is to compute the directional derivative of the function fx,y,z=x2+y2+z2 from point…

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Q: I need a 3d sketch of the equation  Z=x+xsiny+xy

A: z=x+xsiny+xy

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Here we use the formula, Dvf(x,y)=∇f(x,y).v

Q: Find an equation of the tangent plane to the surface z = 2y² – 3x² at the point (-3, -3, -9).

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Q: Consider the curve F(t) that represents the intersection of the surfaces x + y? -1=0 and y= 2x a.…

A: Given: The curve r(t) represents the intersection of the surfaces x2+y2-1=0 and y=z/2x.

Q: Find the directional derivative of o = x2 + 2xyz – yz? at the point (1, 1, 2) in the direction of…

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