The graphs of the functions , , , , and (all blue, with to appearing left-to-right), and (red) and (green) are shown in the following graph.


(Click on the graph for a larger version.)

Suppose that and .
1. Is the area between and from to finite or infinite?


2. Does the integral of from to converge?



3. Does the integral of from to converge?



4. Does the integral of from to converge?



5. Does the integral of from to converge?



6. Does the integral of from to converge?



You can earn partial credit on this problem.