Pre-Calc Homework Solutions 435

Pre-Calc Homework Solutions 435 - Chapter 10 Review 1 tan t...

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Unformatted text preview: Chapter 10 Review 1 tan t sec t equals zero for t k , where k is any 2 dx 1 integer. sec2 t never equals zero. dt 2 dy dt 435 11. 17. (a) (a) Horizontal tangents at 1 tan 2 1 1 tan 0, sec 0 2 2 0, 1 and 2 [ 1.5, 1.5] by [ 1, 1] , 1 sec 2 0, 1 . 2 dx never equals dt (b) 2 18. (a) (b) There are no vertical tangents, since zero. 12. dy dt 2 cos t equals zero for dx dt k , where k is any odd 2 [ 3, 3] by [ 2, 2] (b) 19. (a) integer. integer. 2 sin t equals zero for t k , where k is any (a) Horizontal tangents at and 2 cos 3 3 , 2 sin 2 2 2 cos 2 , 2 sin 2). 2 (0, 2) [ 1.5, 1.5] by [ 1, 1] (0, (b) ( 2, 0) and k , 2 (b) Vertical tangents at ( 2 cos 0, 2 sin 0) ( 2 cos , 2 sin ) (2, 0). 13. dy dt 2 20. (a) 2 sin t cos t sin 2t equals zero for t dx dt where k is any integer. sin t equals zero for t k , [ 1.5, 1.5] by [ 1, 1] where k is any integer. Where they are both zero, use L'Hpital's rule: dy/dt tk dx/dt (b) 21. dy dx f ( ) sin f ( ) cos f ( ) cos f ( ) sin cos 2 cos cos 2 sin lim lim tk sin 2t sin t lim tk 2 cos 2t cos t 2. (0, 0). (a) Horizontal tangent at cos 2 , cos 2 2 sin 2 sin 2 sin 2 cos 2 (b) There are no vertical tangents. 14. dy dt 0, dy dx dy dx 4 , 0, 3 5 , 0, 4 4 2/ 2 and 0, dy dx 7 4 are polar solutions. 2/ 2 9 cos t equals zero for t k , where k is any odd 2 /4 1, 1, dx integer. dt 4 sin t equals zero for t k , where k is 2/ 2 2/ 2 2/ 2 3 /4 1, 1. 5 /4 any integer. (a) Horizontal tangents at 4 cos 4 cos 3 3 , 9 sin 2 2 2 dy dx 2/ 2 2 2 2 2 7 /4 , 9 sin 2 (0, 9) and 22. (4, 0) and The Cartesian equations are y dy dx f ( ) sin f ( ) cos 2 sin 2 sin 2 sin 2 cos 4 sin2 cos 4 cos2 sin 4 sin2 6 cos f ( ) cos f ( ) sin (1 (1 cos 2 )cos cos 2 ) sin x. (0, 9). (b) Vertical tangents at (4 cos 0, 9 sin 0) (4 cos , 9 sin ) ( 4, 0). 15. cos 2 cos3 cos sin 2 cos2 sin sin 2 cos2 sin [ 7.5, 7.5] by [ 5, 5] 4 sin2 2 cos2 . 3 sin 2 16. 0, dy dx [ 7.5, 7.5] by [ 5, 5] 2 and 0, dy dx 3 2 are polar solutions. 4 is undefined, so the tangent lines 0 /2 3 /2 are vertical with equation x 0. ...
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