These are some problems that I'm having trouble with from a review packet. I know the answers, but I don't know how to do them. I would greatly appreciate any help I could get, even if you only help on one or two. I included my work for some of them so you can tell me what I'm doing wrong.

1.) Find lim t --> 0 of [ln(x-9)^8] / [2x - 20]

I used L'hospital's rule a few times and got 0, but the answer is 4. I see 8/2 in the last part, but I thought the ln in the numerator approaches 0...?

2.) The region y = 2x - x^2 and y = 0 is rotated around the x-axis. Find the value of a if the resulting volume is 44π / 3.

The answer is 3, but I get a = 6.5.

3.) It takes 1/200 Joules to stretch a spring from its natural lenth to another y centimeters. It takes 9/200 Joules to stretch the same spring from its natural length to another y + 4 centimeters. Find the value of y. What is the value of the spring constant?

y = 2 and the spring constant is 25. I don't know how to start.

4.) The region bounded by y = 0, x = 0, and y= (3-x) / π is rotated around the y-axis to form a solid of revolution. use the disc method to find the volume.

The answer is 9. I was able to do it with the shell method, but when I used the

disc method, I got some ridiculous answer that included π ^2.

5.) Suppose it is always true that 2 ≤ f' (x) ≤ 4. What is the smallest possible value of f (7) - f (2)?

The answer is 10.