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Unformatted text preview: Math 2312 Homework 1 Due: Wednesday, June 2, 2010 1. Give a verbal description of the subset of real numbers represented by the inequality or interval: a) −∞ ,2 ¡ Solution: The set of all real numbers less than or equal to 2. b) − 1 < ? < 5 Solution: The set of all real numbers between 1 and 5, but not including 1 and 5. c) ≤ ? ≤ 3 Solution: The set of all real numbers between 0 and 3 that also includes 0 and 3. 2. Evaluate: ¢? + 1 ¢ ? + 1 ? < − 1 Solution: Since ¢£¢ = ¤ £ £ ≥ −£ £ < 0 ¥ , then ¢? + 1 ¢ = ¦ ? + 1 ? + 1 ≥ − ? + 1 § ? + 1 < 0 ¥ , or ¢? + 1 ¢ = ¦ ? + 1 ? ≥ − 1 − ? + 1 § ? < − 1 ¥ Therefore, ¢? + 1 ¢ ? + 1 = − ( ? + 1) ? + 1 = − 1 3. Find the distance between a and b. £ = − 126 ? = − 75 Solution: ¢− 126 − ( − 75) ¢ = ¢− 126 + 75 ¢ = ¢− 51 ¢ = 51 4. Use absolute value notation to describe the following: a) (3 pts) The distance between x and 10 is at least 6. Solution: The distance between x and 10 is computed by ¢? − ( − 10) ¢ , so if this distance is to be at least 6, then it can be 6 or greater, i.e., by ¢? − ( − 10) ¢ ≥ 6 b) y is at most 2 units from a Solution: Again, we are concerned with the distance between y and a , ¢¨ − £¢ . Since this distance can be less than 2 units, or equal to 2 units, but not more than 2, then ¢¨ − £¢ ≤ 2 . 5. Evaluate: a) 2 ∙ 4 − 2 2 − 2 ∙ 4 − 1 Solution: 2 ∙ 4 − 2 2 − 2 ∙...
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This note was uploaded on 10/07/2010 for the course MATH 2312 taught by Professor Garrett during the Summer '10 term at Richland Community College.
 Summer '10
 Garrett
 Calculus, Real Numbers

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