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Unformatted text preview: < x < 1 such that f ( x ) = g ( x ). 5. Evaluate: (a) lim x 1cos( x 2 ) x 3 sin x . (b) lim x 0+ x x . (c) lim x sin x + cos xe x log(1 + x 2 ) . 6. Show that n s i =1 i = n ( n + 1) 2 , and use it to prove that i 1 x dx = 1 2 . 1 2 7. Show that n s i =1 i 2 = n ( n + 1)(2 n + 1) 6 , and use it to prove that i 1 x 2 dx = 1 3 . 8. Prove that lim n 1 n k +1 n s i =1 i k = 1 k + 1 , for al l k N ....
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This note was uploaded on 12/27/2011 for the course MATH 118c taught by Professor Garcia during the Fall '09 term at UCSB.
 Fall '09
 Garcia
 Math

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