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Pre-Calc Homework Solutions 357

Pre-Calc Homework Solutions 357 - Chapter 8 Review f(x x...

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25. lim x } g f ( ( x x ) ) } 5 lim x } tan 2 1 1 / x (1/ x ) } 5 lim x 5 lim x } 1 1 1 (1/ x ) 2 } 5 1 f grows at the same rate as g . 26. lim x } g f ( ( x x ) ) } 5 lim x } sin ( 2 1 1 / x ( 2 1 ) / x ) } 5 lim x 5 lim x } 2 ˇ 1 w 2 w x ( w 1 w / x w ) 2 w } 5 ‘ f grows faster than g . 27. (a) lim x 0 f ( x ) 5 lim x 0 } 2 s e in x x 2 2 1 1 } 5 lim x 0 5 ln 2 (b) Define f (0) 5 ln 2. 28. (a) lim x 0 1 f ( x ) 5 lim x 0 1 x ln x 5 lim x 0 1 } l 1 n / x x } 5 lim x 0 1 } 2 1 1 / / x x 2 } 5 lim x 0 1 ( 2 x ) 5 0 (b) Define f (0) 5 0. 29. lim x 5 lim x 1 1 1 } x 1 2 } 2 5 1 # 1 True 30. lim x 5 lim x ( x 2 1 1) 5 ‘ False 31. lim x } x 1 x ln x } 5 lim x 5 1 0 False 32. lim x } ln l ( n ln x x ) } 5 lim x 5 lim x } ln 1 x } 5 0 True 33. lim x } tan 1 2 1 x } 5 } p 2 } # } p 2 } True 34. lim x 5 lim x } x 2 1 1 1 } 5 0 # 1 True 35. lim x 5 lim x } x 2 1 1 1 } 5 0 True 36. lim x } x ln 1 x 1 } 5 lim x 5 0 True 37. lim x } l l n n 2 x x } 5 lim x 5 1 # 1 True 38. lim x } sec 1 2 1 x } 5 } p 2 } # } p 2 } True 39. x 5 3 sin u , dx 5 3 cos u d u , 2 } p 2 } # u # } p 2 } E } ˇ 9 w d 2 w x x w 2 w } 5 E } 3 ) 3 co c s os u u d ) u } 5 E d u 5 u 1 C 5 sin 2 1 } 3 x } 1 C E 3 0 } ˇ 9 w d 2 w x x w 2 w } 5 lim b 3 2 E b 0 } ˇ 9 w d 2 w x x w 2 w } 5 lim b 3 2 3 sin 2 1 } 3 x } 4 5 lim b 3 2 1 sin 2 1 } b
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