SalasSV_08_skillreview

SalasSV_08_skillreview - SKILL MASTERY REVIEW...

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± SKILL MASTERY REVIEW Transcendental Functions and Techniques of Integration Determine whether the function f is one-to-one and, if so, Fnd its inverse. 1. f ( x ) = x 1 / 3 + 2 2. f ( x ) = x 2 x 6 3. f ( x ) = sin 2 x + cos x 4. f ( x ) = 2 x + 1 3 2 x Show that f has an inverse and Fnd ( f 1 ) ± ( c ). 5. f ( x ) = 1 1 + e x ; c = 1 2 6. f ( x ) = 3 x 1 x 3 , x > 0; c = 2 7. f ( x ) = ± x 0 ² 4 + t 2 dt ; c = 0 8. f ( x ) = x π + cos x ; c =− 1 Calculate the derivative. 9. f ( x ) = ( ln x 2 ) 3 10. y = 2 sin ( e 3 x ) 11. g ( x ) = e x 1 + e 2 x 12. f ( x ) = ( x 2 + 1) sinh x 13. y = ln ( x 3 + 3 x ) 14. g ( x ) = tan 1 ( cosh x ) 15. f ( x ) = ( cosh x ) 1 / x 16. f ( x ) = 2 x 3 sin 1 x 2 Evaluate the integral. 17. ± e 1 ln x x dx 18. ± cos x 4 + sin 2 x dx 19. ± 2 x sinh xdx 20. ± ( tan x + cot x ) 2 dx 21. ± x 3 x 2 ( x + 1) dx 22. ± 8 1 x 1 / 3 x 4 / 3 + 1 dx 23. ± sin 2 x cos xdx 24. ± 3 xe 3 x dx 25. ± ln x + 1 dx 26. ± 2
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SalasSV_08_skillreview - SKILL MASTERY REVIEW...

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