Questions from General Calculus

Q: A manufacturer has modeled its yearly production function P (the value

A manufacturer has modeled its yearly production function P (the value of its entire production, in millions of dollars) as a Cobb-Douglas function P (L, K) = 1.47L0.65K0.35 where L is the number of...

Q: A sound with frequency fs is produced by a source traveling along

A sound with frequency fs is produced by a source traveling along a line with speed vs. If an observer is traveling with speed vo along the same line from the opposite direction toward the source, the...

Q: Assume that all the given functions are differentiable. If u

Assume that all the given functions are differentiable. If u = f (x, y), where x = es cos t and y = es sin t, show that

Q: Assume that all the given functions are differentiable. /

Assume that all the given functions are differentiable.

Q: Assume that all the given functions are differentiable. /

Assume that all the given functions are differentiable.

Q: Find the volume of the largest rectangular box in the first octant

Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 2y + 3z = 6.

Q: Find the dimensions of the rectangular box with largest volume if the

Find the dimensions of the rectangular box with largest volume if the total surface area is given as 64 cm2.

Q: Suppose f is a differentiable function of x and y, and

Suppose f is a differentiable function of x and y, and t (u, v) = f (eu + sin v, eu + cos v). Use the table of values to calculate gu (0, 0) and tv (0, 0).

Q: Find the dimensions of a rectangular box of maximum volume such that

Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is a constant c.

Q: The base of an aquarium with given volume V is made of

The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minim...