313 - Department of Mathematics Math 19500 Final...

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Department of Mathematics The City College of CUNY Math 19500 Final Examination May, 2007 Instructions Please show all your work in this booklet. Answer any ten questions from Part I. Answer any ten questions from Part II. This exam contains one question per page. Show your work beneath the question, then fill in the answer box at the top of the page. If you leave out a question, write “OMIT” in the answer box. Show your work for all questions. You can receive partial credit on all questions, including multiple choice questions, provided you show your work. Calculators and other electronic devices are not permitted. Print your name here: _______________________________ Sign your name here: _______________________________ Your instructor’s name: ____________________________ 1
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Part I questions are listed below for your convenience. Choose any ten questions (5 points each). 1. Given x x f - = 1 ) ( and 2 ) ( x x x g - = write )) 2 ( ( )) 2 ( ( f g g f - - as an integer. 2. Find the value of - - 3 1 tan 1 . 3. Given the function 2 2 1 ) ( - - = x x x F , find the inverse function ). ( 1 x F - 4. Find the center C and the radius r of the circle y x y x 4 2 4 2 2 - = - + . 5. Solve the equation 3 ) 4 2 ( log 2 = - x for x. 6. Suppose cot x = 3 4 and sin x is negative. Find sec x . 7. Find the coordinates of the vertex V of the parabola 1 4 2 2 + + - = x x y . 8. Find ( ) 8 log 32 . 9. Find the exact value of π 3 11 sin . 10. Let 2 2 1 ) ( x x x f - - = . Rewrite h h x f h x f ) ( ) ( - - + as a simplified fraction. 11. Rewrite 2 ) 3 ( ) 1 )( 2 ( 1 + - - + - x x x as a simplified sum. 12. Find an equation of the line passing through ) 3 , 4 ( that is perpendicular to the line 5 2 3 = + y x . 2
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On the following pages, answer ten of questions #1 to #12 . Write “OMIT” in the answer boxes for the two questions you leave out. 3
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1. Given x x f - = 1 ) ( and 2 ) ( x x x g - = write )) 2 ( ( )) 2 ( ( f g g f - - as an integer. Write the letter of the correct answer below here __________ (or write “OMIT”). A) 1 B) 2 C) 3 D) 4 E) 5 F) 6 G) 7 H) 8 I) 9 J) None of the above Show your work below! 4
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2. Find the value of - - 3 1 tan 1 . Write the letter of the correct answer here ________(or write “OMIT”) . A) 6 π B) 6 π - C) 6 π ± D) 3 π E) 3 π - F) 3 π ± G) 6 11 π H) 6 11 π ± I) 2 π ± J) None of the above Show your work below!
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This note was uploaded on 10/28/2011 for the course MATH 190 taught by Professor Ocken during the Spring '11 term at CUNY City.

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313 - Department of Mathematics Math 19500 Final...

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