Solve the problem.Integrate

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.

Which is NOT a main argument of the article?

According to Ojha, we should not let Barbie’s flaws deter us from finding her constructive lessons.

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

Find   by using the Chain Rule. Express your final answer in terms of t.

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