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Pre-Calc Homework Solutions 324

# Pre-Calc Homework Solutions 324 - 324 Section 8.1 1 sin t 1...

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7. The limit leads to the indeterminate form 1 . Let ln f ( x ) 5 ln( e x 1 x ) 1/ x 5 } ln( e x x 1 x ) } . lim x 0 1 } ln( e x x 1 x ) } 5 lim x 0 1 5 lim x 0 1 } e e x x 1 1 1 x } 5 } 2 1 } 5 2 lim x 0 1 ( e x 1 x ) 1/ x 5 lim x 0 1 f ( x ) 5 lim x 0 1 e ln f ( x ) 5 e 2 [0, 5] by [0, 10] The graph supports the answer. 8. lim x } x 2 3 x 1 2 1 x 1 3 x 1 } 5 lim x } 3 4 x x 2 1 1 3 1 } 5 lim x } 6 4 x } 5 0 [ 2 5, 25] by [ 2 1, 2] The graph supports the answer. 9. (a) Estimate the limit to be 0. (b) lim x } ln x x 5 } 5 lim x } 5 l x n x } 5 lim x } 5 1 / x } 5 } 0 1 } 5 0 10. (a) Estimate the limit to be } 1 6 } . (b) lim x 0 1 } x 2 x s 3 in x } 5 lim x 0 1 } 1 2 3 x c 2 os x } 5 lim x 0 1 } si 6 n x x } 5 lim x 0 1 } co 6 s x } 5 } 1 6 } 11. Let f ( u ) 5 } s s i i n n 3 4 u u } . Estimate the limit to be } 3 4 } . lim u 0 } s s i i n n 3 4 u u } 5 lim u 0 } 3 4 c c o o s s 3 4 u u } 5 } 3 4 } 12. Let f ( t ) 5 } si 1 n t } 2 } 1 t } 5 } t 2 t si s n in t t } . Estimate the limit to be 0. lim t 0 1 } si 1 n t } 2 } 1 t } 2 5 lim t 0 } t 2 t si s n in t t } 5 lim t 0 } t c 1 os 2 t 1 cos si t n t } 5 lim
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