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# Test 1B - -Ax if x> 2 3 Exercise 3 20 points At what...

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Test 1, Version B Math 1501, Fall 02. Prof. W. Gangbo * September 10, 2002 Name: Instructions. You are to work independently these exercises for the next fourty five minutes (45 mn.). You may not use any textbook or your class notes during the text. Read carefully each exercise and show all your work. * School of Mathematics, Georgia Institute of technology. 1

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Exercise 1 ( 15 points ) Evaluate lim x →- 2 x 2 - 2 x - 8 x + 2 2
Exercise 2 ( 20 points ) For what values of A is f continuous, when f ( x ) = A 2 x 2 if x

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Unformatted text preview: -Ax if x > 2 . 3 Exercise 3 ( 20 points ) At what points is the following function continuous? f ( x ) = ±-7 x if x ∈ N x 2 if x 6∈ N 4 Exercise 4 ( 25 points ) Show that there is a real number c ∈ (1 , √ 7) such that f ( c ) = 0 . Here, f ( x ) = 1 ( x-1) 2 + 1 x-√ 7 . 5 Exercise 5 ( 20 points ) Find the least upper bound and the greatest lower bound for S = { 1 . 4 , 1 . 44 , 1 . 444 , 1 . 4444 , ···} 6...
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