hw82 - 8.2 Pages 432-433 # 1-17odd, 21, 27, 35 1. The limit...

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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 xx x x x x →∞ →∞ = 1000 lim 0 x x →∞ == 11. 1000 1000 1 00 ln lim ( ln ) lim x x →→ = The limit is of the form . 1000 2 999 1 1000 11 1000 ln lim lim 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 ee e →∞ →∞ →∞ = = " 13. 2 22 2 1–cos lim (csc – cot ) lim sin x x = 2 2 0 sin lim 1 sin x x x = = 5. The limit is of the form . 2 3sec 5 3sec tan lim lim tan sec x x x ππ + = 3tan lim lim 3sin 3 sec x x x = 15. 7. The limit is of the form . ( ) 1000 1000 999 1000 ln 1 1000 ln(ln ) lim lim ln x x x x →∞ →∞ = 1000 1000 lim 0 ln x →∞ The limit is of the form 0 0. Let 2 2 (3 ) , then ln ln 3 x yx y x x 2 2 1 ln 3 lim ln 3 lim x x ++ = The limit is of the form . 23 1 2 3 12 000 3 ln 3 lim lim lim – 0 2 x xxx +++ →→→ = 2 ln lim (3 ) lim 1 xy xe = = 9. The limit is of the form . 2 1 2– l n cot – csc lim lim –ln x x x x x = 2 0 l n lim sin x x x x + = 0 2 lim csc – ln sin x x x +    since 0 lim 1 sin x x x + = while 0 lim csc x x + = ∞ and 0 lim – ln . x x + =∞ 17. The limit is of the form 0, which is not an indeterminate form. () tan /2 lim (5cos ) 0 x x x π =
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21. The limit is of the form 0 1, which is not
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hw82 - 8.2 Pages 432-433 # 1-17odd, 21, 27, 35 1. The limit...

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