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Pre-Calc Homework Solutions 422

Pre-Calc Homework Solutions 422 - y 5 e x the exponential...

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11. [ 2 9, 9] by [ 2 6, 6] 12. [ 2 6, 6] by [ 2 4, 4] 13. [ 2 3, 3] by [ 2 2, 2] 14. [ 2 3, 3] by [ 2 2, 2] 15. [ 2 3, 3] by [ 2 2, 2] 16. [ 2 3, 3] by [ 2 2, 2] 17. [ 2 1.8, 1.8] by [ 2 1.2, 1.2] 18. [ 2 3, 3] by [ 2 2, 2] 19. y 5 r sin u , so the equation is y 5 0, which is the x -axis. 20. x 5 r cos u , so the equation is x 5 0, which is the y -axis. 21. r 5 4 csc u r sin u 5 4 y 5 r sin u , so the equation is y 5 4, a horizontal line. 22. r 5 2 3 sec u r cos u 5 2 3 x 5 r cos u , so the equation is x 5 2 3, a vertical line. 23. x 5 r cos u and y 5 r sin u , so the equation is x 1 y 5 1, a line (slope 5 2 1, y -intercept 5 1). 24. x 2 1 y 2 5 r 2 , so the equation is x 2 1 y 2 5 1, a circle (center 5 (0, 0), radius 5 1). 25. x 2 1 y 2 5 r 2 and y 5 r sin u , so the equation is x 2 1 y 2 5 4 y x 2 1 ( y 2 2) 2 5 4, a circle (center 5 (0, 2), radius 5 2). 26. r 5 } sin u 2 5 2 cos u } r sin u 2 2 r cos u 5 5 x 5 r cos u and y 5 r sin u , so the equation is y 2 2 x 5 5, a line (slope 5 2, y -intercept 5 5). 27. r 2 sin 2 u 5 2 2 r 2 sin u cos u 5 2 ( r sin u )( r cos u ) 5 1 x 5 r cos u and y 5 r sin u , so the equation is xy 5 1 1 or, y 5 } 1 x } 2 , a hyperbola. 28. r 5 cot u csc u r sin u 5 cot u y 5 r sin u and } x y } 5 cot u , so the equation is y 2 5 x , a parabola. 29. r 5 csc u e r cos u r sin u 5 e r cos u x 5 r cos u and y 5 r sin u , so the equation is
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Unformatted text preview: y 5 e x , the exponential curve. 30. cos 2 u 5 sin 2 u ( r cos u ) 2 5 ( r sin u ) 2 x 5 r cos u and y 5 r sin u , so the equation is x 2 5 y 2 or y 5 6 x , the union of two lines. 31. r sin u 5 ln r 1 ln cos u r sin u 5 ln ( r cos u ) y 5 ln x , the logarithmic curve. 32. r 2 1 2 r 2 cos u sin u 5 1 r 2 1 2( r cos u )( r sin u ) 5 1 x 2 1 y 2 1 2 xy 5 1 ( x 1 y ) 2 5 1 x 1 y 5 6 1, the union of two lines. 33. r 2 5 2 4 r cos u x 2 1 y 2 5 2 4 x ( x 1 2) 2 1 y 2 5 4, a circle (center 5 ( 2 2, 0), radius 5 2). 34. r 5 8 sin u r 2 5 8 r sin u x 2 1 y 2 5 8 y x 2 1 ( y 2 4) 2 5 16, a circle (center 5 (0, 4), radius 5 4). 35. r 5 2 cos u 1 2 sin u r 2 5 2 r cos u 1 2 r sin u x 2 1 y 2 5 2 x 1 2 y ( x 2 1) 2 1 ( y 2 1) 2 5 2, a circle (center 5 (1, 1), radius 5 ˇ 2 w ). 422 Section 10.5...
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