# Calculus II Exam 2

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 Author: mirahh ID: 264241 Filename: Calculus II Exam 2 Updated: 2014-03-11 02:49:04 Tags: suny geneseo calculus Folders: Description: formulas and whatnot for exam 2 Show Answers:

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• converges only if limit is a number
• converges only if limit is a number
• Diverges if
• only converges if BOTH integrals converge
1. What is the Principle Value of ?
2. What is Euler's Method?
3. What are the important formulas to know for first order linear differential equations?

4. What is the differential equation of Logistic Population Growth?
• or
• k= carrying capacity
• r=intrinsic growth rate
5. 0
6. 1
7.  if
8. 0
9. 0
•  if
• diverges if
•  if
• diverges if
10. What does the convergence test theorem say?
• If  converges, then
• If , then  diverges
11. What is the harmonic series and does it converge/diverge?
• this series diverges even though
12. If  and ,
Then
13. What does the Integral Test say?
• If f(x) is a function on
• and  for n=1,2,3,...
• Then  and  both converge or both diverge
14. What does the Improper Integral Test say?
•  converges if  & diverges if
•  converges if  & diverges if
15. What is the theorem of the basic comparison test?
• Suppose  for all k
• If  diverges, then  diverges
• If  converges, then  converges
16. What is the theorem of the limit comparison test?
• Given , series of positive terms
• Suppose  where
• Then  and  both converge or both diverge

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