Q8: Verify Stokes's Theorem f(x) ds = ff. dr for f = yî+j+xk and the paraboloid for the the surface, S, shown in figure below. z=1-(x² + y²) z≥0 S

Q: Find an equation for the tangent plane to the surface z+1 = ry* cos(z) at the point (1, 1, 0)

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Q: #5, (a) Classify and sketch the surface x+y²+z² = 4, (b) Find the tangent plane at the point…

A: Step 1:a) Classification:This surface is quadratic in three dimensions.It's a type of quadratic…

Q: (4) Find the points Po = (xo, Yo, 2o) on the sphere x? + y? + z² = 9 so that the tangent plane to…

A: Topic- equation of tangent in 3D

Q: I. Evaluate '9 + 3z°dS for the surface S defined by S r(u, v) = [6 cos(u) sin(v), 6 sin(u) sin(v), 3…

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Q: Find an equation of the surface of revolution by revolving the plane curve 3y = v(9- [(x-1)] ^2)…

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Q: 1. Let f(x, y) = ay + y?. (a) Describe the a cross-sections of the surface f. Sketch three of these…

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Q: Consider the surface z = (x + 1)² + (y – 2)² – 1 - Select an equation of the tangent plane to the…

A: we have to find the equation of the tangent plane of the surface 2=(x+1)2+(y-2)2-1 atthe point…

Q: B Suppose we want to find all the points on the surface gx, y) x+ 4y - 4 where the tangent plane is…

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Q: xk N The quadric surfaces 5y = x² and 6z = x² - y² intersect in a curve. Parametrize this curve.…

A: The quadric surfaces 5y=x2 and 6z=x2-y2 x=t

Q: Q2: A. For the surface f derivative at (1,1 derivative and the line to the surface

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Q: b) Find equations for the tangent plane and normal line at the point po on the given surface.…

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Q: L. Let h (x) = f (x) g (x). Find a. h' (1), b. h' (3), and с. h' (4).

A: According to the given information,

Q: Find a parametric representation of the surface in terms of parameters u = x and v = y. NOTE: Enter…

A: a) z+zx2-6y=0b) y2-10z=11

Q: 1. Consider the surface x² + y² - 2xy = x+3y-z = 0 at the point Po(2, -3, 14). Determine the…

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Q: Match the parametrizations to the surfaces shown in the figures. Þ(u, v) = v 4² u cos(v) (u, U) = |…

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Q: Consider the intersection of the surfaces x² + y² = 1 and x + 2y + z = 0. (a) Sketch the surfaces…

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Q: f(z, y) = (z + 2)* - 2(y - 1) - 5. (2,3, 3)

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Q: Suppose A is the vector field A = xi. Calculate A ·î dS using the projection theorem. [You may…

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Q: By sketching the surface that has equation x2 + y2 - z2 = 0, show that the parametric curve r(t) =…

A: Any point on the three dimensional coordinate system is represented using the ordered pair: x, y, z.…