Questions from General Calculus

Q: Write ∬R f (x, y) dA as an

Write ∬R f (x, y) dA as an iterated integral, where R is the region shown and f is an arbitrary continuous function on R.

Q: The cylindrical coordinates of a point are (2√(3 ),

The cylindrical coordinates of a point are (2√(3 ), π/3, 2). Find the rectangular and spherical coordinates of the point.

Q: The rectangular coordinates of a point are (2, 2,

The rectangular coordinates of a point are (2, 2, -1). Find the cylindrical and spherical coordinates of the point.

Q: The spherical coordinates of a point are (8, π/

The spherical coordinates of a point are (8, π/4, π/6). Find the rectangular and cylindrical coordinates of the point.

Q: Identify the surfaces whose equations are given. (a).

Identify the surfaces whose equations are given. (a). θ = π/4 (b). φ = π/4

Q: If [x] denotes the greatest integer in x, evaluate

If [x] denotes the greatest integer in x, evaluate the integral where R = {(x, y) | 1

Q: Write the equation in cylindrical coordinates and in spherical coordinates.

Write the equation in cylindrical coordinates and in spherical coordinates. (a). x2 + y2 + z2 = 4 (b). x2 + y2 = 4

Q: Sketch the solid consisting of all points with spherical coordinates (ρ

Sketch the solid consisting of all points with spherical coordinates (ρ, θ, σ) such that 0 < θ < π/2, 0 < σ < π/6, and 0 < ρ < 2 cos σ.

Q: The speed of sound traveling through ocean water is a function of

The speed of sound traveling through ocean water is a function of temperature, salinity, and pressure. It has been modeled by the function where C is the speed of sound (in meters per second), T is...

Q: Calculate the iterated integral by first reversing the order of integration.

Calculate the iterated integral by first reversing the order of integration.