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lim-know - Some Limits to Know 1 lim x 1 a x x = ea 2 Let k...

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Some Limits to Know 1. lim x →∞ 1 + a x x = e a 2. Let k be a positive integer and let a > 0 . lim x →∞ x k e ax = lim x →∞ k x k - 1 a e ax = . . . = lim x →∞ k ! a k e ax = 0 3. Let k be a positive integer. lim x →∞ (ln x ) k x = lim x →∞ k (ln x ) k - 1 1 x 1 = . . . = lim x →∞ k ! x = 0 . 4. lim n →∞ n n = lim n →∞ n 1 n = lim x →∞ x 1 x = lim x →∞ e lnx x = e 0 = 1 by #3 5. If c is a positive constant, then lim n →∞ n c = lim n →∞ c 1 n = lim x →∞ c 1 x = lim x →∞ e ln c x = e 0 = 1 6. lim x →∞ a x
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