Pre-Calc Homework Solutions 428

Pre-Calc Homework Solutions 428 - 428 dy d Section 10.6 dy...

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Unformatted text preview: 428 dy d Section 10.6 dy d 9. cos sin ( 1 1) sin )cos 10. sin2 cos2 2 cos2 (1 cos cos cos cos )cos sin2 1 (1 cos )sin cos (2 sin sin 2 dx d cos ( 1 sin sin , sin )sin sin 2 cos2 cos 2 dx d sin sin (1 sin 2 dy d 2 cos ) sin 1 4 9 2 sin2 dy d 1 0) or when dx d 0 when cos , 3 1 or , i.e., when 0, , 2 1 2 0 when 5 (2 sin 6 6 3 (cos 2 2 or 5 dx . 3 d 0 when (then sin 0 when (then 1 7 11 , , or 6 6 3 ,r 2 1 2 5 ,r 6 1 2 0) or when 2 cos , 1 0). 2 4 , 3 3 3 sin 2 3 3 5 sin 2 3 3 3 and for 4 3 4 3 0). So there is a horizontal tangent line 3 the line y 2 sin 2 1 4 9 1 or 1, i.e., when 2 for 2 3 5 ,r 3 ,r . So there is a horizontal tangent line for 3 2 sin 2 1 sin 2 6 the line y the line y 2 , for 1 and for 4 6 ,r 3 the line y 2 . There is a vertical tangent line for [the line x line x 3 2 0, r 2], for 2 2 ,r 2 ,r 3 1 2 2 cos 0 2 [again, the again, the line y 1 5 sin 2 6 1 . 4 7 ,r 6 2 cos 2 2], for There is a vertical tangent line for the line x 11 ,r 6 3 7 cos 2 6 [the line x 3 3 and for 4 3 3 11 the line x cos 2 2 6 dx d 3 4 3 . For d dy d d d dx d d dy , 2 d 0, but sin cos cos 1 for 0 for 2 2 cos 2 4 sin and 2 1 2 1 4 1 cos ] and for ,r 2 3 4 3 2 1 2 1 again, the line x cos . 2 3 4 dy dx For , 0, but d d d dy 4 cos sin sin 0 for , and d d d dx 2 cos 2 cos 1 for , d d dy so by L'Hpital's rule 0 and the tangent line is horidx , so by zontal at ,r 0 [the line y 0]. dy is undefined and the tangent line is L'Hpital's rule dx This information can be summarized as follows. Horizontal at: 3 , 2 3 vertical at 2 ,r 0 [the line x 0]. y 3 4 3 , This information can be summarized as follows. Horizontal at: 1 , 2 6 1 5 , 2 6 (0, ) [y 3 5 , 2 3 0], y 2], x x 2] 1 , 4 1 , 4 3 3 4 y y y [x 2 0], x x 1 , 4 1 , 4 Vertical at: (2, 0) [x 1 , 2 1 , 2 2 3 4 3 2, Vertical at: 0, 2 3 2 3 7 , 2 6 3 11 , 2 6 3 3 , 4 3 3 4 (2, 2 ) [x ...
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