PracticeMidtermI

PracticeMidtermI - MAT 319/320 Practice Midterm I Problem...

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Unformatted text preview: MAT 319/320 Practice Midterm I Problem 1. Show by induction that for any natural number n 1 one has 3n > n. Problem 2. Determine the set A of all x in R such that |5.x + 2| < 8. Problem 3. Is the set B = 1 , n2 + 1 n∈N b ounded above? bounded below? Does it have a least upper bound, a greatest lower bound? 1 1 Problem 4. Let Jn = (1 − n , 2 + n ). Prove that Problem 5. Prove that lim Problem 6. Find the limit of 5n + 3 n+7 ∞ n =1 Jn = [1, 2]. =5 . 1 2n + 1 (1 + n2 + 5 ).( n2 + 7 + 2) . 1 ...
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