Questions from General Calculus

Q: Each of these extreme value problems has a solution with both a

Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint....

Q: If a, b, and c are constant vectors, r

If a, b, and c are constant vectors, r is the position vector xi + yj + zk, and E is given by the inequalities 0

Q: Graph the solid that lies between the surfaces z = e^(

Graph the solid that lies between the surfaces z = e^(〖-x〗^2 ) cos (x2 + y2) and z = 2 - x2 - y2 for |x | < 1, |y | < 1. Use a computer algebra system to approximate the volume of this solid correct t...

Q: Express D as a region of type I and also as a

Express D as a region of type I and also as a region of type II. Then evaluate the double integral in two ways. ∬x dA, D is enclosed by the lines y = x, y = 0, x = 1

Q: A 20-ft-by-30-ft swimming pool

A 20-ft-by-30-ft swimming pool is filled with water. The depth is measured at 5-ft intervals, starting at one corner of the pool, and the values are recorded in the table. Estimate the volume of water...

Q: Write the equations in cylindrical coordinates. (a). x2

Write the equations in cylindrical coordinates. (a). x2 - x + y2 + z2 − 1 (b). z = x2 - y2

Q: Sketch the solid described by the given inequalities. r2 <

Sketch the solid described by the given inequalities. r2 < z < 8 - r2

Q: Sketch the solid described by the given inequalities. 2 <

Sketch the solid described by the given inequalities. 2 < ρ < 4, 0 < φ < π/3, 0 < θ < π

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

Sketch the solid described by the given inequalities. ρ < 2, ρ < csc φ

Q: A solid-lies above the cone z = √(x^

A solid-lies above the cone z = √(x^2 + y^2 ) and below the sphere x2 + y2 + z2 = z. Write a description of the solid in terms of inequalities involving spherical coordinates.