lim-know - Some Limits to Know 1 lim x→∞ 1 a x x = ea 2...

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Unformatted text preview: Some Limits to Know 1. lim x→∞ 1+ a x x = ea 2. Let k be a positive integer and let a > 0. lim x→∞ k x k −1 k! xk = lim = . . . = lim k ax = 0 x→∞ a e eax x→∞ a eax 3. Let k be a positive integer. k (ln x) (ln x)k = lim x→∞ x→∞ x 1 lim 1 k −1 1 x = . . . = lim k! = 0. x→∞ x 4. lim √ n n→∞ n = lim n n = lim x x = lim e n→∞ x→∞ x→∞ 1 lnx x = e0 = 1 by #3 5. If c is a positive constant, then √ 1 1 lim n c = lim c n = lim c x n→∞ n→∞ x→∞ = xlim e →∞ ln c x = e0 = 1 a ◦ if j = k b◦ a◦ x k + a1 x k − 1 + · · · + ak = 6. xlim →∞ b xj + b xj −1 + · · · + b 0 if j > k ◦ 1 j ±∞ if j < k 7. nlim n sin →∞ = xlim →∞ 1 1 = xlim x sin →∞ n x 1 x 1 sin x = lim sin θ = 1 by Red #2, p 190 θ→0 θ ...
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This note was uploaded on 05/17/2011 for the course MAC 2312 taught by Professor Bonner during the Spring '08 term at University of Florida.

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