Business Calc Homework w answers_Part_66

Business Calc Homework w answers_Part_66 - 326 Section 8.1...

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26. lim x (ln 2 x 2 ln ( x 1 1)) 5 lim x ln 1 } x 2 1 x 1 } 2 Let f ( x ) 5 } x 2 1 x 1 } . lim x } x 2 1 x 1 } 5 lim x } 2 1 } 5 2 Therefore, lim x (ln 2 x 2 ln ( x 1 1)) 5 lim x ln f ( x ) 5 ln 2 27. lim x 0 1 (ln x 2 ln sin x ) 5 lim x 0 1 ln } sin x x } Let f ( x ) 5 } sin x x } . lim x 0 1 } sin x x } 5 lim x 0 1 } co 1 s x } 5 1 Therefore, lim x 0 1 (ln x 2 ln sin x ) 5 lim x 0 1 ln f ( x ) 5 ln 1 5 0 28. lim x 0 1 1 } 1 x } 2 } ˇ 1 x w } 2 5 lim x 0 1 } 1 2 x ˇ x w }5‘ 29. The limit leads to the indeterminate form 1 . Let f ( x ) 5 ( e x 1 x ) 1/ x . ln ( e x 1 x ) 1/ x 5 } ln ( e x x 1 x ) } lim x 0 } ln ( e x x 1 x ) }5 lim x 0 5 2 lim x 0 ( e x 1 x ) 1/ x 5 lim x 0 e ln f ( x ) 5 e 2 30. The limit leads to the indeterminate form 0 . Let f ( x ) 5 1 } x 1 2 } 2 x . ln 1 } x 1 2 } 2 x 5 x ln 1 } x 1 2 } 2 5 lim x 0 5 lim x 0 5 lim x 0 2 x 5 0 lim x 0 1 } x 1 2 } 2 x 5 lim x 0 e ln f ( x ) 5 e 0 5 1 31. lim x 6‘ } 2 x 2 3 x 2 2 x 5 1 2 lim x 6‘ } 4 x 3 2 1 } 5 0 32. lim x 0 } t s a i n n 1 7 1 x x } 5 lim x 0 } 11 7 s c e o c s 2 7 1 x 1 x }5} 1 7 1 } 33. The limit leads to the indeterminate form 0 . Let f ( x ) 5 (ln x ) 1/ x . ln (ln x ) 1/ x 5 } ln (l x n x ) } lim x } ln (l x n x ) } 5 lim x 5 lim x } x l 1 n x } 5 0 lim x (ln x ) 1/ x 5 lim x e ln f ( x ) 5 e 0 5 1 34. The limit leads to the indeterminate form 0 . Let f ( x ) 5 (1 1 2 x ) 1/(2 ln x ) . ln (1 1 2 x ) 1/(2 ln x ) 5 } ln ( 2 1 l 1 n x 2 x ) } lim x } ln ( 2 1 l 1 n x 2 x ) lim x 5 lim x } 1 1 x 2 x } 5 lim x } 1 2 } 5 } 1 2 } lim x (1 1 2 x ) 1/(2 ln x ) 5 lim x e ln f ( x ) 5 e 1/2 5 ˇ e w 35. The limit leads to the indeterminate form 0 0 . Let f ( x ) 5 ( x 2 2 2 x 1 1) x 2 1 ln ( x 2 2 2 x 1 1) x 2 1 5 ( x 2 1) ln ( x 2 2 2 x 1 1) 5 lim x 1 5 lim x 1 5 lim x 1 5 lim x 1 2 2( x 2 1) 5 0 lim x 1 ( x 2 2 2 x 1 1) x 2 1 5 lim x 1 e ln f ( x ) 5 e 0 5 1 36. The limit leads to the indeterminate form 0 0 . Let f ( x ) 5 (cos x ) cos x . ln (cos x ) cos x 5 (cos x ) ln (cos x ) 5 } ln s ( e c c os x x ) } lim x p /2 2 } ln s ( e c c os x x ) }5 lim x p /2 2 5 lim x p /2 2 } se 2 c t x a t n an x x } 5 lim x p /2 2 2 cos x 5 0 lim x p /2 2 (cos x ) cos x 5 lim x p /2 2 e ln f ( x ) 5 e 0 5 1 } 2 co si s n x x } }} sec x tan x } 2 ( x ( x 2 2 1 1 ) 2 ) } }} 2 } ( x 2 1 1) 2 } } x 2 2 2 x 2 2 x 2 1 1 } }} 2 } ( x 2 1 1) 2 } ln ( x 2 2 2 x 1 1) }} } x 2 1 1 } ln ( x 2 2 2 x 1 1) }} } x 2 1 1 } } 1 1 2 2 x } } } 2 x } } l 1 n / x x } } 1 } 2 1 2 / x / x 2 3 } } 2 1/ x 2 ln 1 } x 1 2 } 2 } } 1 x } ln 1 } x 1 2 } 2 } } 1 x } } e e x x 1 1 1 x } } 1 326 Section 8.1
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37. The limit leads to the indeterminate form 1 . Let f ( x ) 5 (1 1 x ) 1/ x . ln (1 1 x ) 1/ x 5 } ln (1 x 1 x ) } lim x 0 1 } ln (1 x 1 x ) }5 lim x 0 1 } 5 1 lim x 0 1 (1 1 x ) 1/ x 5 lim x 0 1 e ln f ( x ) 5 e 1 5 e 38. The limit leads to the indeterminate form 1 . Let f ( x ) 5 x 1/( x 2 1) . ln x 1/( x 2 1) 5 } x ln 2 x 1 } lim x 1 } x ln 2 x 1 } 5 lim x 1 } 1 1 / x } 5 1 lim x 1 x 1/( x 2 1) 5 lim x 1 e ln f ( x ) 5 e 1 5 e 39. The limit leads to the indeterminate form 0 0 .
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This document was uploaded on 10/31/2011 for the course MAC 2311 at University of Florida.

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Business Calc Homework w answers_Part_66 - 326 Section 8.1...

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