CalcNotes0203-page31

CalcNotes0203-page31 - (Section 2.3: Limits and Infinity I)...

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(Section 2.3: Limits and Infinity I) 2.3.31 The limit of this sequence (as the number of digits of ± approaches ± ) is taken to be 2 . It turns out that 2 ² 8.82498 . However, defining ± 2 () ² is more problematic. For example, ± 2 3.1 = ± 2 31 10 . We are looking for a 10 th root of ± 2 31 . From Precalculus, we know that ± 2 31 has ten distinct 10 th roots in ± , the set of complex numbers. Refer to DeMoivre’s Theorem for the complex roots of a complex number. See The Math Forum @ Drexel: Ask Dr. Math, Meaning of Irrational Exponents . 6. Dominant terms. We will say that x d “dominates” x n as x ±² for real constants d and n ± d > n . This is because the growth of the (absolute value of) x d makes the growth of the (absolute value) of x n seem negligible by comparison in the “long run.” More precisely, lim x x n x d = lim x x n ³ d = 0 ± d > n . (If d > n , the denominator of x n x d “explodes more dramatically” than the numerator does., and the limit is 0 as x .) • Also, lim x ±²³ x n x d = ± ( d > n , and x n and x d
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This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.

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