luate the surface integral. // (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = u – v, z = 1 + 2u + v, o sus 3, 0 s v

Q: Find parametric equations for the line through the point P(3, 6, 4) that is parallel to the plane x…

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Q: Match each parametrization with the corresponding surface. (i) (ii) (iii) (iv) (v) Answer Bank (u,…

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Q: Find and equatin for the parabolid z = x^2+y^2 in spherical coordinates

A: Given query is to find equation of paraboloid in spheo coordinates.

Q: 36 for 0 <= u <= 6 and 0 <= v <= 2(pi) where <= is less then equal too where pi = 3.1415

A: Introduction: An ellipse is the locus of all points that satisfy the equations.x = a sint,  y = b…

Q: The parametric equations I= 11 + (I2- 1)t, y=y+ (y2- y1)t where 0<t< 1 describe the line segment…

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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: 5 25- y² 50-g² –y² Convert (x² + y² + z²)dzdædy into spherical coordinates. ²+y² 5/2 pª cos ødpdød0…

A: Answer:We have to convert∫50∫25-y20∫50-x2-y2x2+y2x2+y2+z2 dzdxdy into sphercal coordinates∵0≤y≤5…

Q: Find an equation for the plane tangent to the level surface x² + y? +z = 4 at the point Po(1,1, 2).…

A: Solving

Q: Find polar coordinates (r, 0) of the point (1, -V3), where r <0 and 0 s0 < 2m

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Q: 6. Find parametric equations for the line of intersection of the planes 2x – y + z = 4 and 3x + y +…

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Q: d the polar coordinates if (x, y) = (-√3, 1), r≥ 0, -2π < E

A: Given query is to find the polar coordinates.

Q: y2 f(x, y)dx dy Let f(x, y) = e-x2-y² and

A: answer is in next step