Questions from General Calculus

Q: Find the absolute maximum and minimum values of f on the set

Find the absolute maximum and minimum values of f on the set D. f (x, y) = e-x2-y2 (x2 + 2y2); D is the disk x2 + y2 < 4

Q: Use the change of variables formula and an appropriate transformation to evaluate

Use the change of variables formula and an appropriate transformation to evaluate ∬R xy dA, where R is the square with vertices (0, 0), (1, 1), (2, 0), and (1, -1).

Q: The Mean Value Theorem for double integrals says that if f is

The Mean Value Theorem for double integrals says that if f is a continuous function on a plane region D that is of type I or II, then there exists a point sx0, y0 d in D such that Use the Extreme Va...

Q: Use Lagrange multipliers to find the maximum and minimum values of f

Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint(s). f (x, y) = x2y; x2 + y2 = 1

Q: (a). Evaluate ∬D 1/((x^2+

(a). Evaluate ∬D 1/((x^2+y^2 )^(n/2) ) dA, where n is an integer and D is the region bounded by the circles with center the origin and radii r and R, 0 < r < R. (b). For what values of n does the inte...

Q: Use Lagrange multipliers to find the maximum and minimum values of f

Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint(s). f (x, y, z) = xyz; x2 + y2 + z2 = 3

Q: Use Lagrange multipliers to find the maximum and minimum values of f

Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint(s). f (x, y, z) = x2 + 2y2 + 3z2; x + y + z = 1, x - y + 2z = 2

Q: Find the points on the surface xy2z3 = 2 that are closest

Find the points on the surface xy2z3 = 2 that are closest to the origin.

Q: A package in the shape of a rectangular box can be mailed

A package in the shape of a rectangular box can be mailed by the US Postal Service if the sum of its length and girth (the perimeter of a cross-section perpendicular to the length) is at most 108 in....

Q: Shoe that ∫_0^∞(arctan πx-arctanx)/x dx

Shoe that ∫_0^∞(arctan πx-arctanx)/x dx=π/2 lnπ by first expressing the integral as an iterated integral.