Questions from General Calculus

Q: Find the dimensions of an open rectangular glass tank of volume 32

Find the dimensions of an open rectangular glass tank of volume 32 cubic feet for which the amount of material needed to construct the tank is minimized. [See Fig. 4(a).] Figure 4:

Q: A shelter for use at the beach has a back, two

A shelter for use at the beach has a back, two sides, and a top made of canvas. [See Fig. 4(b).] Find the dimensions that maximize the volume and require 96 square feet of canvas. Figure 4:

Q: Draw the level curves of heights 0, 1, and 2

Draw the level curves of heights 0, 1, and 2 for the function. f (x, y) = 2x - y

Q: Let f (x, y) be any production function where

Let f (x, y) be any production function where x represents labor (costing $a per unit) and y represents capital (costing $b per unit). Assuming that $c is available, show that, at the values of x, y t...

Q: By applying the result in Exercise 25 to the production function f

By applying the result in Exercise 25 to the production function f (x, y) = kxayb, show that, for the values of x, y that maximize production, we have (This tells us that the ratio of capital to lab...

Q: Solve the exercise by the method of Lagrange multipliers. Minimize

Solve the exercise by the method of Lagrange multipliers. Minimize x2 + 3y2 + 10, subject to the constraint 8 - x - y = 0.

Q: Solve the exercise by the method of Lagrange multipliers. Maximize

Solve the exercise by the method of Lagrange multipliers. Maximize x2 - y2, subject to the constraint 2x + y - 3 = 0.

Q: Solve the exercise by the method of Lagrange multipliers. Maximize

Solve the exercise by the method of Lagrange multipliers. Maximize x2 + xy - 3y2, subject to the constraint 2 - x - 2y = 0.

Q: Find the formula (of the type in Check Your Understanding Problem

Find the formula (of the type in Check Your Understanding Problem 1) that gives the least-squares error for the points (2, 6), (5, 10), and (9, 15).

Q: Find the formula (of the type in Check Your Understanding Problem

Find the formula (of the type in Check Your Understanding Problem 1) that gives the least-squares error for the points (8, 4), (9, 2), and (10, 3).