1. Parametrize the following surfaces: (a) The portion of the plane x+y+z = 1 which lies in the first octant. (b) z + x² + y² = 1 where z ≥ 0. (c) S is given by +4 +2²=1.

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: Find the angle between the surfaces x² + y² + z² = 41 and z = x² + y²-11 at the point (4, 0, 5):

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Q: III. Find a set of parametric equations for the curve of intersection of the cylinder (x-1)² + ² x²…

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Q: Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?

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Q: Determine the parametric equations of the curve of intersection of the paraboloid x? – y? + z² = 0…

A: Detailed explanation mentioned below

Q: Find the parametric equations for the line through the point of intersection of the lines L1:x = 2 +…

A: In line L1 and L2  't' is used as parameter but don't confuse with it. Different different line we…

Q: 1) let L be the line of intersection of the planes x+y+z=6 and x-y + 2z = 0. Find parametric…

A: To find the parametric equation for the line through the point that is perpendicular to the line of…

Q: / (2² + y²) do, where S is the portion of the sphere r? + y? + z² = 9 in the first octant that is…

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Q: Exercise 8.3.52: For each of the following nonlinear systems, i. Find all critical points…

A: As per bartleby by rules for this  question only first is to be answered please upload the subpart…

Q: Use hyperbolic functions to parametrize the intersection of the surfaces x² - y² = 4 and z = 5xy.…

A: Use hyperbolic functions to parametrize the intersection of the surfaces  and (Use symbolic notation…

Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y z 1…

A: Given: