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hw82 - 8.2 Pages 432-433 1-17odd 21 27 35 1 The limit is of...

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8.2 Pages 432-433 # 1-17odd, 21, 27, 35 1. The limit is of the form . 1000 999 1000 1 1000 ln lim lim 1 x x x x x x →∞ →∞ = 1000 lim 0 x x →∞ = = 11. 1000 1000 1 0 0 ln lim ( ln ) lim x x x x x x = The limit is of the form . 1000 2 999 1 1000 1 1 0 0 1000 ln lim lim x x x x x x x = 0 lim –1000 0 x x = = 3. The limit is of the form . 10000 9999 10000 lim lim 10000! lim 0 x x x x x x x x e e e →∞ →∞ →∞ = = = = " 13. 2 2 2 2 0 0 1– cos lim (csc – cot ) lim sin x x x x x x = 2 2 0 sin lim 1 sin x x x = = 5. The limit is of the form . 2 2 2 3sec 5 3sec tan lim lim tan sec x x x x x x x π π + = 2 2 3tan lim lim 3sin 3 sec x x x x x π π = = = 15. 7. The limit is of the form . ( ) 1000 1000 999 1 1 1000 ln 1 1000 ln(ln ) lim lim ln x x x x x x x x →∞ →∞ = 1000 1000 lim 0 ln x x x →∞ = = The limit is of the form 0 0 . Let 2 2 (3 ) , then ln ln3 x y x y x x = = 2 2 1 0 0 ln3 lim ln3 lim x x x x x x + + = The limit is of the form . 2 3 1 2 3 1 2 0 0 0 3 ln3 lim lim lim – 0 2 x x x x x x x x + + + = = = 2 ln 0 0 lim (3 ) lim 1 x y x x x e + + = = 9.
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