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.
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Continuity, Differentiability and the Volume of a Solid are investigated.