Unformatted text preview: / ( x 4 + 16) . (2) Show that the equation x = 1 + Z x cos( t ) t 2 + 4 dt has one and only one solution. (3) Recall that (by deﬁnition) lim x →∞ f ( x ) = L if and only if for every real number ± > 0 there is a real number x such that  f ( x )L  < ± for all x > x . Prove the following: lim x →∞ f ( x ) = L if and only if lim t → + f (1 /t ) = L. (4) Show that for any real number c , lim x →∞ ± x + c xc ² x = e 2 c . 1...
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 Fall '08
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 Math, Cauchy sequence, lim x+c xc

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