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Unformatted text preview: 6. Find a function f such that f ( x ) = x 3 and the line x + y = 0 is tangent to the graph of f . 7. A paticle is moving with acceleration a ( t ) = cos t + sin t . Given that s (0) = 0 and v (0) = 5, ﬁnd the position of the particle. 8. Determine a region whose area is equal to lim n →∞ ∑ n i =1 2 n (5 + 2 i n ) 10 . 9. Find an expression for the area under the curve y = x 3 from 0 to 1 as a limit and use the formula 1 + 2 3 + 3 3 + · · · + n 3 = [ n ( n +1) 2 ] 2 to evaluate the limit. 1...
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 Spring '10
 Tor
 Math

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