1110-fa2009-final-exam

# Example where true example where false math 1110 fall

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Example where true Example where false

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Math 1110 (Fall 2009) Final Exam (12/10/2009) 8 Question 4 continued. The following statements are true for some functions and false for others. For each statement, give a function where the statement is true, and a function where the statement is false. Give a one-sentence explanation of why each example works or does not work. You may use an equation, a graph, or both to describe your example functions. (c) A parametric curve is not the graph of a function. Example where true Example where false (d) If f ( x ) and g ( x ) are continuous on [ 1, 2 ] then f ( x ) g ( x ) is continuous on [ 1, 2 ] . Example where true Example where false
Math 1110 (Fall 2009) Final Exam (12/10/2009) 9 Question 5. (24 points/8 points each) FOUR of the important theorems that we learned this semester are The Sandwich Theorem The Intermediate Value Theorem The Mean Value Theorem The Fundamental Theorem of Calculus. Please identify which theorem proves each of the THREE following facts. Be sure to justify your answer in a complete sentence (or two)! (a) Professor Holm was once π feet tall. (b) There is a function whose derivative is cos ( e x ) tan - 1 ( x ) sin 2 ( x ) + 52 . (c) lim x →∞ sin ( x ) x = 0

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Math 1110 (Fall 2009) Final Exam (12/10/2009) 10 Question 6. (10 points) Concepts that we have discussed this semester have showed up recently in the U.S. economic news. (a) In July 2009, the U.S. economy supported 135 million jobs. The Labor Department has re- cently announced revised job loss numbers for the past several months, shown in the table below. On the axes below, sketch the graph that shows the total number of jobs in the U.S. labor market. Month Jobs lost August 2009 200,000 September 2009 139,000 October 2009 111,000 November 2009 11,000 Jobs Aug 09 Sep 09 Oct 09 Nov 09 Jul 09 time 134.0 134.5 135.0 (in millions) (b) In early November, President Obama announced that while the U.S. economy was still losing jobs, the rate of job loss had slowed. Please express this statement mathematically, using the
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• Fall '06
• MARTIN,C.
• 12/10/2009

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