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Unformatted text preview: MA115 Mathematical Analysis I Test 1 Instructions The test consists of two sections, Part 1: Questions 1 6 Part 2: Questions 7 10 You are to do all of Part 1. For Part 2, select and complete 2 of the 4 problems given. Please clearly indicate which two problems you choose. The two problems you indicate will be the only problems from Part 2 graded. Show your work. This does not mean your answers should be longwe just need you to tell us how you obtained your answer in addition to what you obtained. Any response to a question consisting of just an answer will be marked incorrect. Please type your answers up as you do your homework, and submit your completed test via email by 9PM Wednesday, July 7, to the course instructor and the two teaching assistants. You are allowed to use your textbook and all of the notes from the course. Good luck! 1 Part 1 1. (10 points) (a) For f ( x ) = x 2 we have f ( x + h ) f ( x ) h = ( x + h ) 2 x 2 h = x 2 + 2 xh + h 2 x 2 h = 2 xh + h 2 h = 2 x + h (b) From part (a), lim h f ( x + h ) f ( x ) h = lim h (2 x + h ) = 2 x 2. (10 points) (a) The domain of H ( x ) = 1 ln x is { x  < x e } . Two parts of the function H ( x ) influence the domain: the square root and the natural log. Since we cant take the square root of a negative number we must have 1 ln x Solving this inequality gives x e . But also, since we cant take the logarithm of any number less than or equal to zero, we must have x > 0....
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This note was uploaded on 04/07/2008 for the course MA 115 taught by Professor Mahalanobis during the Fall '08 term at Stevens.
 Fall '08
 Mahalanobis
 Math

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