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Unformatted text preview: Find lim n →∞ L n and lim n →∞ R n . These limits should be the same, and their common value is the area of the region. Solution. Following the hint, lim n →∞ L n = lim n →∞ 1-e n (1-e 1 /n ) Write h = 1 /n . So lim n →∞ L n = lim n →∞ 1-e n (1-e 1 /n ) = (1-e ) lim h → + h 1-e h = (1-e )(-1) ³ lim h → + e h-1 h ´-1 The limit in the parentheses is the derivative of f ( x ) = e x at a = 0. We know that limit is 1. Hence lim n →∞ L n = e-1 Since R n = e 1 /n L n , we have lim n →∞ R n = ± lim n →∞ e 1 /n ²± lim n →∞ L n ² = 1 · ( e-1) 2...
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This note was uploaded on 07/19/2010 for the course MATHEMATIC V63.0121 taught by Professor Leingang during the Spring '09 term at NYU.
- Spring '09