Pre-Calc Homework Solutions 429

Pre-Calc Homework Solutions 429 - Section 10.6 11. y dy d...

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Unformatted text preview: Section 10.6 11. y dy d 429 2 sin2 4 sin 2 sin 2 cos 12. dy d 4 sin2 4(sin 2 (3 cos 2 4 cos )cos ) 3 cos 4 4 cos )sin 8 cos2 cos dx d 3 cos (3 3) 3 sin 3 x 2 sin sin 2 4 sin cos sin (8 cos 4 sin 2 0, 2 dy d dy d 2 cos 2 0 when , dx , and d 0 when 3 , . They are never both zero. 4 4 dy d 0 when cos 137 16 , i.e., when 0.405, 2.146, 4.137, or 5.878 (values solved for with a graphing calculator). (then sin 2 cos 1 For 0, 2 , the curve has horizontal asymptotes 0 sin 0 0], 2, 0]. For 2, 4 2 2 3 , the curve has 4 4 dx d 0 when cos 1 0, 3 8 or 2 1.186 or 3 0). So there 0.676 2.146, at (0, 0) [y (0, ) [ y y 2 sin 2 , and 0) or when 3 8 0 sin 5.097 (then 8 cos vertical asymptotes at 3 2, 4 [x 1 . 2 cos 4 1] and is a horizontal tangent line for [the line y r 0.676 sin 0.405 0.405, r 0.267], for x 3 2 cos 4 This information can be summarized as follows. Horizontal at: (0, 0) [y 2, 2 5.176 [the line y 4.137, r 5.176 5.176 sin 2.146 4.343], for 0], 2], 0] [x [x 1], 1] [y [the line y 5.878, r [the line y tangent for for r ,r 5.176 sin 4.137 0.676 0.676 sin 5.878 0, r 4.343], and for (0, ) [y Vertical at: 2, 4 3 2, 4 0.267]. There is a vertical 1 cos 0 7], for 1], for 1], 2 , 1 [the line x 7 cos 1 cos 2 7 [the line x 1 [again, the line x cos 2 1 3 9 the line x , and for 2 16 3 3 9 cos 1 ,r again, the line x . 8 2 16 3 ,r 8 This information can be summarized as follows. Horizontal at: ( 0.676, 0.405) [y (5.176, 2.146) [y (5.176, 4.137) [y ( 0.676, 5.878) [y Vertical at: ( 1, 0) [x (1.5, 1.186) (7, ) [x (1.5, 5.097) ( 1, 2 ) [x x 7], x 9 , 16 0.267], 4.343], 4.343], 0.267] 1], 9 , 16 1] ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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