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Pre-Calc Homework Solutions 327

# Pre-Calc Homework Solutions 327 - Section 8.1 37 The limit...

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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 . Let f ( x ) 5 (sin x ) x . ln (sin x ) x 5 x ln (sin x ) 5 lim x 0 1 5 lim x 0 1 5 lim x 0 1 } 2 x s 2 in co x s x } 5 lim x 0 1 5 0 lim x 0 1 (sin x ) x 5 lim x 0 1 e ln f ( x ) 5 e 0 5 1 40. The limit leads to the indeterminate form 0 0 . Let f ( x ) 5 (sin x ) tan x ln (sin x ) tan x 5 tan x ln (sin x ) 5 } ln c ( o si t n x x ) } lim x 0 1 } ln c ( o si t n x x ) } 5 lim x 0 1 5 lim x 0 1 ( 2 sin x cos x ) 5 0 lim x 0 1 (sin x ) tan x 5 lim x 0 1 e ln f ( x ) 5 e 0 5 1 41. The limit leads to the indeterminate form 1 2‘ .
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