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Unformatted text preview: 5. Consider the Function f ( x ) = 1 1 + x 2 , x R . Prove, using the defnition, that (a) lim x f ( x ) = 0 . (1) (b) f is uniFormly continuous. 6. Given the convergent sequences { a n } n N R and { b n } n N R , let a R and b R be the corresponding limits, i.e., lim n a n = a ; lim n b n = b. Prove, using the defnition oF limit, the Following statements: (a) lim n ( a n + b n ) = a + b . (b) lim n a n b n = ab . (c) IF b 6 = 0, lim n a n b n = a b . 7. Prove the Following statement: A Function f : I R is continuous at x I iF and only iF { x n } n N I such that x n x , it Follows that f ( x n ) f ( x )....
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This document was uploaded on 12/27/2011.
 Fall '09
 Math

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