Consider: . What Type of Improper Integral Is This? How Do We Handle This Type? Evaluate

Exam 3 Review
Supplemental Instruction
IowaStateUniversity / Leader: / Mason
Course: / Math 166
Instructor: / Bolles
Date: / 3/23/2015

1. Using:

Find:

1. Consider: . What type of improper integral is this? How do we handle this type? Evaluate the Integral.

1. What conditions must be met to state anything about whether a function converges or diverges using a direct comparison test? Use this to determine whether the function:
   Diverges or coverages?

1. What happens when the result of the limit comparison tests yields an “L” value that is 0? What can be said about the two functions if it is 0? Use a limit comparison test to test if converges or diverges. What about: ?

1. Consider for what values of “q” does the integral converge? This is also called the ____ series test. Use this to determine if the following integrals are convergent or divergent:

1. Consider: what type of improper integral is this? To what values does the value “p” make the series convergent? Hint: try the following numbers for p: 0.5, 1, 2.

1. Evaluate the limits: .
   Now consider:
   What can we say about the convergence or divergence of these series? Based on this information?

1. Consider the sequence: 5 – 5/4 + 5/16 – 5/64+……. What type of series would this correlate to? How do we determine the value of which this series would converge to? If the series converges find the value to which this series would converge to.

1. Find the sums of the series:

1. Determine if the series following series coverages

1. Does the sequence 1/9+1/27+1/81+…. Diverge or converge?

1. Does the series coverage or diverge? If so what value would the nth partial sum be? (not the infinite sum)

1. What is the difference between the following series?
   

1. Use the integral test to prove whether the following series converge or diverges:

1. Final notes:
   -Go over all of the theorems presented that we’ve covered and pay attention to the wording of definitions
   -For comparisons I usually write out the first few terms to make sure one of my functions is greater/less than the other.
   -Know your integration techniques. They are fair game at any point.
   -If you know the “p” test well it will make your life easier
   -Use multiple tests on series if you have the time to further clarify
   -This is probably the hardest Math 166 exam (just saying) so be prepared!