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Unformatted text preview: lim sup n ( x n + y n ) < lim sup n x n + lim sup n y n . (3) Suppose that lim n y n exists. Prove that lim sup n ( x n + y n ) = lim sup n x n + lim n y n . 4. [10 points] Find lim sup n x n and lim inf n x n in the following cases: (1) x n = sin( n/ 4). (2) x n = 1 + 1 n n cos( n ) . 5. [10 points] Let x n = sin( n ). Find lim sup n x n . 1...
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This document was uploaded on 02/22/2011.
 Spring '09
 Real Numbers

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