Use cylindrical coordinates to find the volume of the indicated region.the region enclosed by the paraboloids z = x2 + y2 – 9 and z = 63 – x2 – y2.  

Find the volume by using polar coordinates.The region bounded by the paraboloid z = x2 + y2 ,  the cylinder x2 + y2 = 64, and the xy-plane.

Solve the problem.Let R ={(x, y): 1 ≤ x < 5, 0 ≤ y < 6}. Evaluate  

Evaluate the double integral over the given region.

Find the volume by using polar coordinates.The region bounded by the paraboloid z = x2 + y2, the cylinder x2 + y2 = 25, and the xy-plane.

Ken, Barbie’s boyfriend, has a central role in her life.

Ojha ultimately argues for a doll that showcases Barbie’s positives while avoiding her negatives.

Solve the problem.Find the equation for the tangent plane to the surface x2 + 6xyz + y2 = -4z2  at the point (-1, -1, -1).

Find the absolute maxima and minima of the function on the given domain. f(x, y) = 2×2 + 6y2  on the disk bounded by the circle x2 + y2 = 9 

Find the linear approximation of the function at the given point.