Questions from General Calculus

Q: (a). Use a graphing calculator or computer to graph the

(a). Use a graphing calculator or computer to graph the circle x2 + y2 = 1. On the same screen, graph several curves of the form x2 + y = c until you find two that just touch the circle. What is the s...

Q: Find the extreme values of f subject to both constraints.

Find the extreme values of f subject to both constraints.

Q: Change from rectangular to cylindrical coordinates. (a). (-

Change from rectangular to cylindrical coordinates. (a). (-1, 1, 1) (b). (-2, 2 3 , 3)

Q: Change from rectangular to cylindrical coordinates. (a). (-√(

Change from rectangular to cylindrical coordinates. (a). (-√(2 ), √(2 ), 1) (b). (2, 2, 2)

Q: Describe in words the surface whose equation is given. φ

Describe in words the surface whose equation is given. φ = π/3

Q: Describe in words the surface whose equation is given. ρ2

Describe in words the surface whose equation is given. ρ2 - 3ρ + 2 = 0

Q: Find the image of the set S under the given transformation.

Find the image of the set S under the given transformation. S = {(u, v) | 0 < u < 3, 0 < v < 2}; x = 2u + 3v, y = u - v

Q: Find the image of the set S under the given transformation.

Find the image of the set S under the given transformation. S is the square bounded by the lines u = 0, u = 1, v = 0, v = 1; x = v, y = u (1 + v2)

Q: Find the image of the set S under the given transformation.

Find the image of the set S under the given transformation. S is the triangular region with vertices (0, 0), (1, 1), (0, 1); x = u2, y = v

Q: Write the equation in spherical coordinates. (a). z

Write the equation in spherical coordinates. (a). z = x2 + y2 (b). z = x2 - y2