Pre-Calc Homework Solutions 468

Pre-Calc Homework Solutions 468 - 468 Appendix A6 ex 2 e x...

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Unformatted text preview: 468 Appendix A6 ex 2 e x x 2 2. sinh x 1 4 cosh x 3 16 9 sinh x cosh x 1 tanh x 25 9 4 3 5 3 1 5 , 3 4 , 5 sinh2 x 1 4 2 3 12. cosh2 x 1 x (e 4 sinh2 x e x ex 2 e x x 2 ) (e x e ) (e x 1 (4) 4 x 3 1 3 e 1 ) (e x e x ) 1 (2e x )(2e x ) 4 1 (4e 0) 4 tanh x 13. y 1 cosh x 3 , 5 6 sinh dy x dx 3 6 cosh dy dx 2 cosh x 3 coth x 5 , sech x 4 3 4 14. y and csch x 1 sinh x 1 sinh (2x 2 1) 1 [cosh (2x 2 1)](2) cosh (2x cosh2 x 64 225 8 , 15 1 tanh x 1 sinh x 15 8 1) t 2t 1/2 tanh t 1/2 1 1/2 t (2t 1/2) 2 t 3. cosh x 17 ,x 15 0 sinh x 289 225 8 15 17 15 1 15. y 2 dy dt t tanh 17 2 15 1 1 [sech2(t 1/2)] 2 (tanh t 1/2)(t 1/2 ) sech 8 , coth x 17 15 , and csch x 17 t 1 t 1 tanh t tanh x sinh x cosh x 16. y t 2 tanh [sech2 (t sech2 1 t t 2 tanh t )]( t 2 1 dy dt 1 17 , sech x 8 1 cosh x )(t 2) 1 t (2t)(tanh t ) 2t tanh dy dz dy dz 4. cosh x 169 25 13 ,x 5 0 sinh x 144 25 12 5 13 5 cosh2 x 1 17. y 18. y ln (sinh z) ln (cosh z) (sech )(1 1 sinh x cosh x 12 , 5 12 , coth x 13 5 , and csch x 13 1 tanh x cosh z sinh z sinh z cosh z coth z tanh z tanh x 19. y 1 sinh x 5 12 ln sech ) (sech ) ln sech ) tanh )(1 ln sech )] ln sech ) 13 , sech x 12 1 cosh x dy d sech tanh sech In Exercises 510, graphical support may consist of showing that the graph of the original expression minus the simplified one is the line y 0. 5. 2 cosh (ln x) 2 e e ln x 2 e 2 x4 1 2x 2 2 ln x ( sech sech (sech (sech tanh tanh )(1 (sech (1 e ln x e ln x e ln x 2 1 e ln x e 2 lnx 2 x 1 x tanh )[1 tanh )(ln sech ) ln csch ) csch coth csch 2 ln x 6. sinh (2 ln x) x2 2 1 x2 20. y (csch )(1 dy d (csch ) (1 csch 7. cosh 5x 8. cosh 3x 9. (sinh x 10. ln (cosh x sinh 5x sinh 3x cosh x)4 sinh x) e 5x 2 e3x 2 ex e 5x e 5x 2 e 3x 2 ex 2 e 5x e 5x e 3x ln csch )( csch coth (1 1 coth ) coth ) e 3x e 3x ln csch )(csch ln csch ) (csch e 4x 21. y (csch ln cosh x dy dx coth )(1 e 2 x e x 4 (e x)4 coth )(ln csch ) ln (cosh x ln 1 x) 0 sinh x) ln (cosh2 x sinh2 x) 1 tanh2 x 2 1 sinh x (2 tanh x)(sech2 x) 2 cosh x 11. (a) sinh 2x sinh (x 2 sinh x cosh x sinh x cosh x cosh x cosh x cosh x sinh x sinh x sinh x tanh x (tanh x)(sech2 x) tanh3 x (tanh x)(1 sech2 x) (tanh x)(tanh2 x) (b) cosh 2x cosh (x x) cosh2 x sinh2 x ...
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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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