Pre-Calc Homework Solutions 469

Pre-Calc Homework Solutions 469 - Appendix A6 1 coth2 x 2...

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Unformatted text preview: Appendix A6 1 coth2 x 2 cosh x 1 (2 coth x)( csch2 x) sinh x 2 469 22. y ln sinh x dy dv 31. y csch x) 2 cos 1x dy dx 1 1 x2 x sech 1 1 x 1 x 1 x2 1 coth x (coth x)(csch x) 2 2 (coth x)(1 1 x2 1 1 x (1) sech x sech 1 x (coth x)(coth x) 23. y (x (x 2 2 coth x (x (x 2 2 3 x2 sech 1 1 1 x 1) sech (ln x) 2 1) x x 1 e ln x 2x 1) 2 1 x 1) 2 e ln x 32. y dy 2x dx 2 ln x ln x (1 1 x 1 x 1 x 2 sech x x 1 1 x2 1 x 2)1/2 sech (1 1 (1 2 x 1 x2 2 dy dx 1 x x 2)1/2 x 24. y (4x 2 (4x 2 1) csch (ln 2x) 1) 4 1 (4x 2 (4x 2 1) 1) x ) 2 1/2 ( 2x) sech x 1 x x x2 e ln 2x e 1 ln 2x 2x 2 (2x) 4x 4x 2 sech 1 sech 1 x 1 4x 33. y dy dx csch 1 1 2 ln 1 2 1 2 1 2 2 25. y sinh dy dx x sinh 1 (x 1/2 ) 1 x 1 1 x 1/2 2 2 x(1 x) dy d 1 2 x 1 1 2 1 1 1 (x 1/2 )2 ln (1) ln (2) 1 2 2 1 ln 2 1 dy d dy dx 1 2 2 26. y cosh (2 x 1) 1) 1)1/2]2 1/2 cosh (2(x 1 1)1/2 ) 34. y 4x 3 1 (2) dy dx 1 4x 2 1 (x 2 csch 2 (ln 2)2 2 1 (2 ) sec2 x 2 ln 2 1 22 [2(x 1 x 1 35. y 7x 3 1 sinh sec2 x 1 (tan x) sec2 x sec x 27. y (1 ) tanh (1 ) tanh 2 sec2 x 1 2 1 (tan x)2 sec x sec x sec x sec x (sec x)(tan x) sec2 x 1 dy d 1 1 1 1 ( 1) tanh 1 36. y cosh 1 (sec x) dy dx (sec x)(tan x) tan2 x 1 (sec x)(tan x) tan x 1 sec x, 0 dy dx x 2 28. y ( dy d 2 2 ) tanh ( 2 ( 1 ( 1) 1)2 1 37. (a) If y (2 ( 1) 2) tanh 1 tan (sinh x) cosh x cosh2 x C, then 2 ) (2 1 1 ( 1) 1 cosh x sinh2 x sech x, which verifies the 2 2 2 2) tanh ( t 1) (1 1/2 formula. (b) If y sin 1 1 (2 29. y (1 dy dt 1 2 t 2) tanh t) coth 1 t) coth 1 (tanh x) 2 C, then sech2 x 1 (t 1/2 ) tanh x sech2 x sech x dy dx sech x, which verifies the formula. (1 t) (1/2)t 1 (t 1/2 )2 1 ( 1) coth 1 (t 1/2 ) 38. If y dy dx x2 sech 1 x 2 coth t 1 x sech x sech 1 1 x x 1 2 x 1 x2 2 1 2 1 x2 C, then 2x 4 1 x2 x, which verifies the formula. 1 30. y (1 dy dt t 2) coth (1 2t coth t 2) 1 t 1 t2 1 ( 2t) coth 1 t 39. If y dy dx x2 2 coth 1 1 x x 2 1 t x coth x x 2 1 2 1 C, then 1 x2 1 2 x coth 1 x, which verifies the formula. ...
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