Questions from General Calculus

Q: A region R in the xy-plane is given. Find

A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u- and v-axes. R is bounded...

Q: A region R in the xy-plane is given. Find

A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u- and v-axes. R is the par...

Q: Find the extreme values of f on the region described by the

Find the extreme values of f on the region described by the inequality.

Q: A region R in the xy-plane is given. Find

A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u- and v-axes. R lies betwe...

Q: A region R in the xy-plane is given. Find

A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u- and v-axes. R is bounded...

Q: Use the given transformation to evaluate the integral. ∬R

Use the given transformation to evaluate the integral. ∬R (x - 3y) dA, where R is the triangular region with vertices (0, 0), (2, 1), and (1, 2); x = 2u + v, y = u + 2v

Q: Use the given transformation to evaluate the integral. ∬R

Use the given transformation to evaluate the integral. ∬R (4x + 8y) dA, where R is the parallelogram with vertices (-1, 3), (1, -3), (3, -1), and (1, 5); x = 1/4 (u + v), y = 1/4 (v - 3u)

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 inside the circle (x – 1)2 + y2 = 1 and outside the circle x2 + y2 = 1

Q: Use a triple integral to find the volume of the given solid

Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the coordinate planes and the plane 2x + y + z = 4

Q: Use a triple integral to find the volume of the given solid

Use a triple integral to find the volume of the given solid. The solid enclosed by the paraboloids y = x2 + z2 and y = 8 - x2 - z2