Questions from General Calculus

Q: Describe in words the surface whose equation is given. θ

Describe in words the surface whose equation is given. θ= π/6

Q: Sketch the solid whose volume is given by the integral and evaluate

Sketch the solid whose volume is given by the integral and evaluate the integral. ∫_(-π/2)^(-π/2) ∫_0^2 ∫_0^(r^2)r dz dr dθ

Q: Identify the surface whose equation is given. r = 2

Identify the surface whose equation is given. r = 2 sin θ

Q: Sketch the solid described by the given inequalities. 0 <

Sketch the solid described by the given inequalities. 0 < θ < π/2, r < z < 2

Q: Sketch the solid whose volume is given by the integral and evaluate

Sketch the solid whose volume is given by the integral and evaluate the integral. ∫_0^2 ∫_0^2π ∫_0^r r dz dθ dr

Q: Use spherical coordinates. Evaluate ∭E y2z2 dV, where

Use spherical coordinates. Evaluate ∭E y2z2 dV, where E lies above the cone φ = π/3 and below the sphere ρ = 1.

Q: Leonhard Euler was able to find the exact sum of the series

Leonhard Euler was able to find the exact sum of the series in Problem 5. In 1736 he proved that In this problem we ask you to prove this fact by evaluating the double integral in Problem 5. Start b...

Q: Find the mass and center of mass of the solid E with

Find the mass and center of mass of the solid E with the given density function ρ. E is the cube given by 0 < x < a, 0 < y < a, 0 < z < a; ρ(x, y, z) = x2 + y2 1 z2

Q: A model for the density δ of the earth’s atmosphere near its

A model for the density δ of the earth’s atmosphere near its surface is δ = 619.09 2 0.000097ρ where δ (the distance from the center of the earth) is measured in meters and is measured in kilograms pe...

Q: Use a double integral to find the area of the region.

Use a double integral to find the area of the region. The region inside the cardioid r = 1 + cosθ and outside the circle r = 3 cosθ