Find the point P(x, y, z) at which the paraboloid has a tangent plane parallel to the plane (x, y, z) = y = 3x² + ₂2 5x+6y+z= 4.

Q: (b) Find the surface area of the portion of the paraboloid given by the equation z = 1- x? – y? that…

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Q: ind positive constants b and n, such that 3n + 2 n.

A: Finding the values of b and no

Q: Find the regions of the (x, y)-plane where the equation (1+ x) + 2xy; Əxðy + 2y? 2 + x xy? + (1 –…

A: Given equation is, 1+x∂2u∂x2+2xy∂2u∂x∂y+2y2∂2u∂y2+x2∂u∂x-xy2∂u∂y+(1-y)u=0 The equation…

Q: At what point on the paraboloid y = x² + z² is the tangent plane parallel to the plane 3x + 2y + 3z…

A: Introduction: Let z=f(x, y) be the equation of a surface S in R3, and let P=(a, b, c) be a point on…

Q: Evaluate e dz where C is the line segment from 0 to 2+2i, parametrized by z(t) = t + it?.

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Q: Calculate dz – yz dy – sen(2)dz, where Cis the path connecting the point A(-2, 2, 4) to the point…

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Q: The points on the surface x2−2y2−3z2 = 33 at which the tangent plane is parallel to the 8x+4y+6z=5…

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Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

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Q: Find a vector parametric equation for the ellipse that lies on the plane 4x - 4y + z = -7 and is…

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Q: Find the equation for the sphere centered M(2,-3,2) tangent to the D:6x-3y+2z-11=0 plane

A: we have to find the equation for the sphere centered 2,-3,2 and tangent to the plane 6x-3y+2z-11=0.