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Unformatted text preview: lim n →∞ n X i =1 2 n ± 5 + 2 i n ² 10 5. a ) Use Deﬁnition 2(page 320 in Stewart) to ﬁnd an expression for the area under the curve y = x 3 from 0 to 1 as a limit. b ) The following formula for the sum of the cubes of the ﬁrst n integers is proved in Appendix E(A34 in Stewart).Use it to evaluate the limit in part (a). 1 3 + 2 3 + 3 3 + ,...,n 3 = ³ n ( n + 1) 2 ´ 2 1...
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This note was uploaded on 04/30/2010 for the course MATHEMATIC MATH 119 taught by Professor Tor during the Spring '10 term at Middle East Technical University.
 Spring '10
 Tor
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