Determine whether the following statements are true and give an explanation or counterexample.

a. A region R is revolved about the y-axis to generate a solid S. To find the volume of S, you could use either the disk/washer method and integrate with respect to y or the shell method and integrate with respect to x.

b. Given only the velocity of an object moving on a line, it is possible to find its displacement, but not its position.

c. If water flows into a tank at a constant rate (for example, 6 gal/min), the volume of water in the tank increases according to a linear function of time.

d. The variable y = t + 1 doubles in value whenever t increases by 1 unit.

e. The function y = Ae^0.1t increases by 10% when t increases by 1 unit.

f. ln xy = (ln x)(ln y).

g. 

Transcribed Image Text:

- 1 sinh(In x) 2x