# 313 - Department of Mathematics Math 19500 Final...

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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
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
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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