I have been going through some practice questions online to prepare for my midterm and ran into a few questions I had problems with but for which there where no explanations for solving.

1. Find limit of as approaches infinity.

I thought all that would matter in this question is the magnitude of x as I couldn't see any reasonable way to simplify the equation. I answered 1, but the answer is actually 3. What can I do to this problem to make it more manageable?

2. For the given function and values of , and find the largest open interval about on which the inequality holds. Then determine the largest value for z > 0 such that .

, , ,

I worked through all of my textbook questions and never saw something worded like this. I did some work but none of my solutions were close to those that are given. I really have no idea where to start with this question. The answers are: The inequality holds for (6.92, 7.08) and the largest value of is 0.08.

3. .

This is part of a larger word problem; however, every step I followed up to this point matched the process in the answer book. Whenever I took the derivative of v using the quotient rule I would come up with an ugly looking quadratic instead of this elegant solution. What am I doing wrong?