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A1.1. Use the substitution at = asinhu to work out the integral t f (a2 moi/2a; U A12. (i) Show that the Laplace transform of

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A1.1. Use the substitution at = asinhu to work out the integral t f (a2 moi/2a; U A12. (i) Show that the Laplace transform of f (:1?) = a: is 3%. (ii) Show by induction that the Laplace transform of \"i is 1 n! 3n+1 ' (You may assume that R\"+Ie_3R > 0 as R > 00 for 3 > 0.) [4]

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