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Exam2Fall2011Solution

# Exam2Fall2011Solution - Name PIN MATH 4093-010 Exam 2 You...

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Unformatted text preview: Name: PIN: MATH 4093-010 Exam 2 You must show all your work in a clear, clutter free format to receive full credit on each problem. This is a closed book test. Please do your final work on either the paper provided or “clean” lined paper and staple this cover sheet to the front of your work. Remember to leave room for the staple when writing up your work. (1) (5 pts) Carefully define the following: lim n →∞ a n = a iff ∀ ϵ > , ∃ N ∈ N ∋ n > N ⇒ | a n − a | < ϵ (2) (10 pts) Define the following terms in a way consistent with the definitions given in class (or the book): (a) sequence is a function from the natural numbers to the real numbers. (b) A sequence is bounded if ... there exists M > such that the magnitude of each term in the sequence is less than M . (3) (15 pts) State the following theorems: (a) The Order Limit Theorem If a n ≤ b n for all n in the natural numbers, then lim a n ≤ lim b n , provided the limits exist....
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Exam2Fall2011Solution - Name PIN MATH 4093-010 Exam 2 You...

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