iez_1 A power series representation off [H 3 d3 about t = Dis 2 an") _1 where an (t) = I I. Check The interval of convergence of z) = 2:1 % - 9:" is: using the notation 00(a.b] for (11,33), 0c(a,b} for (a, b]. co(a,b} for [(1, b}. cc(a.b) for [5, 5]. Wm"): Suppose you are given the following information: I{%) = 1 3%) = 5 r"{%) = 5-2 fruig] = _5I Extrapolating the pattern to general 71. we find that f{"3(%] = |:'. We want to nd a function f(I) verifying the above conditions. We may consider the Taylor's series associated to x] 2 63(1 B)", n_EI where on = l B =' '. Comparing this series with that of a known function. it turns out that we can take x) = :l. Check