Questions from General Calculus

Q: For what values of the number r is the function continuous on

For what values of the number r is the function continuous on R3?

Q: (a). Find inequalities that describe a hollow ball with diameter

(a). Find inequalities that describe a hollow ball with diameter 30 cm and thickness 0.5 cm. Explain how you have positioned the coordinate system that you have chosen. (b). Suppose the ball is cut in...

Q: Set up iterated integrals for both orders of integration. Then evaluate

Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order and explain why it’s easier. ∬D y2 exy dA, D is bounded by y = x, y = 4, x = 0

Q: Evaluate the double integral by first identifying it as the volume of

Evaluate the double integral by first identifying it as the volume of a solid.

Q: Find the area of the finite part of the paraboloid y =

Find the area of the finite part of the paraboloid y = x2 + z2 cut off by the plane y = 25. [Hint: Project the surface onto the xz-plane.]

Q: The figure shows the surface created when the cylinder y2 + z2

The figure shows the surface created when the cylinder y2 + z2 = 1 intersects the cylinder x2 + z2 = 1. Find the area of this surface.

Q: The joint density function for a pair of random variables X and

The joint density function for a pair of random variables X and Y is (a). Find the value of the constant C. (b). Find P (X (c). Find P (X + Y

Q: Find the Jacobian of the transformation. x = 2u +

Find the Jacobian of the transformation. x = 2u + v, y = 4u - v

Q: Find the Jacobian of the transformation. x = u2 +

Find the Jacobian of the transformation. x = u2 + uv, y = uv2

Q: Find the Jacobian of the transformation. x = s cos

Find the Jacobian of the transformation. x = s cos t, y = s sin t