( x + 1) 2 = ( y + 3)

Transcription

1 f(x + h) f(x) h 0 f(x) = 1 1 Simplify the difference quotient, if, for. h 5 x 1 ( 5 x+h ) ( 5 x) 1 h( 5 x) 2 1 ( 5 x+h ) ( 5 x) 1 ( 5 x h) ( 5 x) 1 h( 5 x) 1 ( 5 x h) ( 5 x) 2 Write an equation for the given graph if the point ( 2, 2) is on the curv ( x + 1) 2 = y + ( x 1) 2 = y ( x + 1) 2 = ( y + ) ( y + ) 2 = ( x + 1) ( y ) 2 = ( x 1) ( x 1) 2 = ( y ) PAGE 1

2 Find equations of two successive vertical asymptotes of the graph of f( x ) = tan 1 2 x x = x = x = x = x = x = 5, x = 5, x =, x = 5, x = 5, x = 5 5, x = 4 A ship is 11 miles east and 4 miles south of a harbor. What bearing should be taken to sail directly to the harbor? S arctan 11 4 W S arctan 4 11 E N arctan 11 4 W N arctan 4 11 W S arctan 11 4 E N arctan 11 4 E PAGE 2

3 5 A roof truss is made in the shape of an inverted asymmetrical V. The lengths of the two edges are 5 meters and 11 meters respectively. The edges meet at the peak making a 0 angl a) Find the width of the truss meters meters 14 meters 91 meters 9 55 meters 9 meters b) Find the height of the peak. 55 meters meters meters meters meters meters 2 9 PAGE

4 Find the EXACT value of tan 1 tan Find all solutions to the given equation in the interval 0, 2 ). cos( 2x ) + sin 2 x = 0 8 Find an equation in x and y that has the same graph as the polar equation. r 2 sin ( 2 ) = x = y x + y = y = x x y = x y = x + y = PAGE 4

5 9 Find the solutions of the equation that are in the interval 0, 2 ). 2 cos 2 x + sin x = 0 10 Find the foci and asymptotes for the given coni x 2 y 2 2x 4y 4 = 0 Foci: ( 0, 2), ( 2, 2) Asymptotes: y + 2 = ( x 1) Foci: ( 1 2, 2) Asymptotes: y + 2 = ( x + 1) Foci: ( 2, 2), ( 4, 2) Asymptotes: y 2 = ( x 1) Foci: ( 1 2, 2) Asymptotes: y 2 = ( x + 1) Foci: ( 1 2, 2) Asymptotes: y + 2 = ( x 1) Foci: ( 1 2, 2) Asymptotes: y 2 = ( x 1) 11 tan 2 arccos 5 = PAGE 5

6 12 For the given parametric equations, find the x/y-equation. x = t 2 14t + 49, y = t x = ( y ) 2 14 ( y ) + 49 x = y = x y = x 2 x = y 2 y 2 14 y x = y 2 14 ( y + ) sin = PAGE

7 14 For the given graph of f(x), as x 1 +,f( x) f( x ) does not approach any value as x 1 +. sec 2 t 15 is equivalent to which of the following? tan t csc t sin t cos t sec t csc t cos t sin t cot t none of the above PAGE

8 1 All asymptotes, intercepts, and holes of a rational function f are shown in the figur Select an equation for f( x ) = ( x 4) ( x ) ( x + 1) ( x + 5) f( x ) = ( x + 4) ( x 1) ( x 1) ( x 5) f( x ) = ( x 4) ( x + 1) ( x + 5) 2 f( x ) = ( x + 5) ( x + 1) ( x + 1) ( x 4) f( x ) = ( x 4) ( x + 1) ( x + 1) ( x + 5) f( x ) = ( x + 4) ( x + ) ( x 1) ( x 5) 1 Suppose that a robotic arm can rotate between 1 = 20 and 2 = 100. If the length of the arm can vary between 4 inches to 20 inches, find the area of the work spac 2040 in in 2 in 2 in in 2 1 in 2 PAGE 8

9 18 Find all solutions to the given equation in the interval 0, 2 ). tan = 5 = arctan( 5), = 2 arctan( 5) = + arctan( 5), = 2 arctan( 5) = arctan( 5), = 2 arctan( 5) = + arctan( 5), = 2 arctan( 5) = arctan( 5), = 2 arctan( 5) = arctan( 5), = arctan( 5) 19 cos sin = PAGE 9

10 20 The Ellipse is a park in Washington, D.C. It is bounded by an elliptical path with a major axis of length 40 m and a minor axis of length 400 m. Find the distance between the foci of this ellips m 5100 m m m m m 21 sin 5 2 = tan 4 = 22 Find all solutions of the equation. sec = 2 = 5 = + 2 n, = + 2 n + 2 n, = n = n, = n = 2 = 2 = + n, = 4 + n + 2 n, = n + n, = 11 + n PAGE 10

11 2 Insulation must be put into the space between 2 concentric cylinders. Write a function for the volume V between the inner and outer cyllinders if the inner cylinder has a radius 5 feet, the outer cylinder has radius x feet, and both cylinders are 9 feet high. V( x) = 9 x ( x + 10 ) V( x) = 9 ( x 5) 2 V( x) = ( x + 5) ( x 5) V( x ) = 9 x 2 V( x) = 9 ( x 5) ( x + 5) V( x) = 18 ( x 5) 24 Match each graph in the left-hand column with its equation on the right. y = 2 cos( x ) y = 2 sin( x ) y = 2 cos( 2x ) y = 2 sin( x ) y = 2 cos( x ) y = 2 sin( 2x ) PAGE 11

12 ANSWER KEY Final Fall f 2. f. e 4. c 5. d c. e,, e e 11. b 12. e c 14. a 15. c 1. e 1. b 18. e 19. b 20. f 21. 1; e 2. e 24. y = 2 sin( x ), y = 2 cos( x ) ANSWER KEY - Page 1