Continuity, Differentiability and the Volume of a Solid
November 15th, 2022
Please see attached file for full problem description.
1. Decide whether each of the following statements is true or false. If true, explain why. If false, give a counter-example and explain why the counter-example contradicts the statement.
a. If then
b. If f and g are continuous functions on [a,b], then
c. If f and g are differentiable and on [a,b], then on [a,b].
2. Any cross-section of a particular solid cut by a plane perpendicular to the x-axis is a square whose diagonal lies on the parabolas y2 = 4x and x2 = 4y. Find the volume of the solid.