Questions from General Calculus

Q: Consider the problem of maximizing the function f (x, y

Consider the problem of maximizing the function f (x, y) = 2x + 3y subject to the constraint √x + √y = 5. (a). Try using Lagrange multipliers to solve the problem. (b). Does f (25, 0) give a larger va...

Q: The latitude and longitude of a point P in the Northern Hemisphere

The latitude and longitude of a point P in the Northern Hemisphere are related to spherical coordinates ρ, θ, φ as follows. We take the origin to be the center of the earth and the positive z-axis to...

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 enclosed by both of the cardioids r = 1 + cosθ and r = 1 - cosθ 

Q: Consider a square fan blade with sides of length 2 and the

Consider a square fan blade with sides of length 2 and the lower left corner placed at the origin. If the density of the blade is ρ (x, y) = 1 + 0.1x, is it more difficult to rotate the blade about th...

Q: Sketch the region whose area is given by the integral and evaluate

Sketch the region whose area is given by the integral and evaluate the integral. ∫_(π/2) ^ ∫_0^ (2 sinθ)r dr dθ

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

Use a double integral to find the area of the region. One loop of the rose r = cos 3θ 

Q: (a). A lamina has constant density ρ and takes the

(a). A lamina has constant density ρ and takes the shape of a disk with center the origin and radius R. Use Newton’s Law of Gravitation (see Section 13.4) to show that the...

Q: Determine whether the statement is true or false. If it is

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. 1. If y1 and y2 are solutions of y'' + y = 0,...

Q: (a). Write the general form of a second-order

(a). Write the general form of a second-order homogeneous linear differential equation with constant coefficients. (b). Write the auxiliary equation. (c). How do you use the roots of the auxiliary equ...

Q: Determine whether or not the vector field is conservative. If it

Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = ∇f. F (x, y, z) = ex sin yz i + zex cos yz j + yex cos yz k