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Pre-Calc Homework Solutions 355

Pre-Calc Homework Solutions 355 - Chapter 8 Review 2 dz 1...

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50. E } 1 1 d s x in x } 5 E 5 E } z 2 1 2 2 d z z 1 1 } 5 E } ( z 2 1 d 1 z ) 2 } 5 2 } z 1 2 1 } 1 C 5 2 1 C 51. E } 1 2 d c x os x } 5 E 5 E } d z z 2 } 5 2 } 1 z } 1 C 5 2 1 C 52. E } 1 2 d s u in u } 5 E 5 E } z 2 2 2 2 d z z 1 1 } 5 E } ( z 2 2 d 1 z ) 2 } 5 2 } z 2 2 1 } 1 C 5 2 1 C 5 1 C 53. E } 1 1 sin d t t 1 cos t } 5 E 5 E } z 1 dz 1 } 5 ln ) z 1 1 ) 1 C 5 ln ) tan } 2 t } 1 1 ) 1 C Chapter 8 Review Exercises (pp. 454–455) 1. lim t 0 } t 2 ln t ( 2 1 1 2 t ) } 5 lim t 0 5 ‘ for t 0 2 and 2‘ for t 0 1 The limit does not exist. 2. lim t 0 } t t a a n n 3 5 t t } 5 lim t 0 } 3 5 s s e e c c 2 2 3 5 t t } 5 } 3 5 } 3. lim x 0 } 1 x 2 si c n os x x } 5 lim x 0 } x cos s x in 1 x sin x } 5 lim x 0 5 2 4. The limit leads to the indeterminate form 1 . f ( x ) 5 x 1/(1 2 x ) ln f ( x ) 5 } 1 ln 2 x x } lim x 1 } 1 ln 2 x x } 5 lim x 1 } 2 1/ 1 x } 5 2 1 lim x 1 x 1/(1 2 x ) 5 lim x 1 e ln f ( x ) 5 e 2 1 5 } 1 e } 5. The limit leads to the indeterminate form 0 . f ( x ) 5 x 1/ x ln f ( x ) 5 } ln x x } lim x } ln x x } 5 lim x } 1 1 / x } 5 0 lim x x 1/ x 5 lim x e ln f ( x ) 5 e 0 5 1 6. The limit leads to the indeterminate form 1 . f ( x ) 5 1 1 1 } 3 x } 2 x ln f ( x ) 5 x ln 1 1 1 } 3 x } 2 5 lim x 5 lim x 5 lim x } x 3 1 x 3 } 5 3 lim x 1 1 1 } 3 x } 2 x 5 lim x e ln f ( x ) 5 e 3 7. lim r } c l o n s r r } 5 0 since ) cos r ) # 1 and ln r as r . 8. lim u p /2 1 u 2 } p 2 } 2 sec u 5 lim u p /2 5 lim u p /2 } 2 s 1 in u } 5 2 1 u 2 } p 2 } } cos
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