a) Evaluate ds, where the curve C is the intersection between the surface z = V1- y? and the plane r = 3 starting from (3, 1,0) to (3. –1,0). TM

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A: Given that

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Q: a) Evaluate x²y? ds, where the curve C is the intersection between the surface z = := V1– y? and the…

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A: We have to find the surface integral ∫sxds.

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A: We have to find the equation of tangent plane.

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A: We have to find partial derivatives first.

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Q: Q3/ Sketch the surface z 3x2 + y? +1 and find its linear approximation at P.(0,-1).

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Q: Which of the following is the equation of the tangent plane of the z = 3x^2+x-y^2+y surface at the…

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Q: Find the equation of the plane tangent Z= x2+ Y2 at point P (1,2,5) to the surface

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Q: 7. Consider the Surface S:z = 52² + 5y?. An equation of the plane tangent to Sat the point P (3, 3,…

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Q: Find the plane tangent to the surface z=x+ y at the point (3,4,25). a. 6x+8y-z=25 b. 6x-8y-z=25 c.…

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Q: Let C be the curve of intersection of the cylinder x2+y? = 2 and the hyperbolic paraboloid x? – y? +…

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Q: The tangent plane to the graph of the surface z=In(x2+y²) at the point (1,0,0) contains point…

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Q: Use Stoke’s Theorem to evaluate the line integral ∮C(z2−y2)dx +(x2−z2)dy +(y2−x2)dz, where the curve…

A: Given equation of the curve is ∮C(z2-y2)dx+x2-z2dy+(y2-x2)dz ,the equation of the paraboloid…