SalasSV_07_07_ex - EXERCISES 7.7 Determine the exact value....

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Unformatted text preview: EXERCISES 7.7 Determine the exact value. 1. (a) tan − 1 0; (b) sin − 1 ( − √ 3 / 2). 2. (a) arc sec 2; (b) tan − 1 ( √ 3). 3. (a) cos − 1 ( − 1 2 ) ; (b) sec − 1 ( − √ 2). 4. (a) sec (sec − 1 [ − 2 / √ 3]); (b) sec (arccos[ − 1 2 ]). 5. (a) cos (sec − 1 2); (b) arctan (sec 0). 6. (a) arcsin (sin [11 π/ 6]); (b) arctan (tan [11 π/ 4]). 7. (a) cos − 1 (sec [7 π/ 6]); (b) sec − 1 (sin [13 π/ 6]). 8. (a) cos ( sin − 1 [ 3 5 ] ) ; (b) sec ( tan − 1 [ 4 3 ] ) . 9. (a) sin ( 2 cos − 1 [ 1 2 ] ) ; (b) cos ( 2 sin − 1 [ 4 5 ] ) . 10. (a) cos ( sin − 1 [ 1 2 ] + sin − 1 [ − 1] ) ; (b) tan ± sin − 1 [ √ 2 / 2] + cos − 1 [ 1 2 ] ² . Differentiate the function. 11. y = tan − 1 ( x + 1). 12. y = tan − 1 √ x . 13. f ( x ) = sec − 1 (2 x 2 ). 14. f ( x ) = e x sin − 1 x . 15. f ( x ) = x sin − 1 2 x . 16. f ( x ) = e tan − 1 x . 17. u = (sin − 1 x ) 2 . 18. v = tan − 1 ( e x ). 19. y = tan − 1 x x . 20. y = sec − 1 √ x 2 + 2. 21. f ( x ) = √ tan − 1 2 x . 22. f ( x ) = ln (tan − 1 x ). 23. y = tan − 1 (ln x ). 24. g ( x ) = sec − 1 (cos x + 2). 25. θ = sin − 1 ( √ 1 − r 2 ). 26. θ = sin − 1 ³ r r + 1 ´ . 27. g ( x ) = x 2 sec − 1 ³ 1 x ´ . 28. θ = tan − 1 ³ 1 1 + r 2 ´ . 29. y = sin [sec − 1 (ln x )]. 30. f ( x ) = e sec − 1 x . 31. f ( x ) = √ c 2 − x 2 + c sin − 1 ± x c ² , c > 0. 32. y = x √ c 2 − x 2 − sin − 1 ± x c ² , c > 0, 33. Show that for a > (7.7.11) µ dx ¶ a 2 − ( x + b ) 2 = sin − 1 ³ x + b a ´ + C . 34. Show that for a ±= (7.7.12) µ dx a 2 + ( x + b ) 2 = 1 a tan − 1 ³ x + b a ´ + C . 35. (a) Verify (7.7.10). (b) Show that for a > µ dx ( x + b ) ¶ ( x + b ) 2 − a 2 = 1 a sec − 1 ³ | x + b | a ´ + C . Give the domain and range of each function, and verify the dif-ferentiation formula. 36. f ( x ) = cos − 1 x ; d dx (cos − 1 x ) = − 1 √ 1 − x 2 . 37. f ( x ) = cot − 1 x ; d dx (cot − 1 x ) = − 1 1 + x 2 . 38. f ( x ) = csc − 1 x ; d dx (csc − 1 x ) = − 1 | x | √ x 2 − 1 . Evaluate the integral....
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This note was uploaded on 10/12/2010 for the course MATH 12345 taught by Professor Smith during the Spring '10 term at University of Houston - Downtown.

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SalasSV_07_07_ex - EXERCISES 7.7 Determine the exact value....

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