About the sequence keZ we have the following a x 1 EB xo b

Last updated: 10/8/2023

About the sequence keZ we have the following a x 1 EB xo b for each 1 to b t b MKk b 1 x 1 te to b t b k20 k 1 x keZ is uniformly Cauchy on t b to b verification of these properties is left for the reader We consider the uniform limit of the sequence x 10 8 to 8 B x b C which is given by 1 l b to b Thus X 1 lim x x t lim x 1 1 2 f s X s ds Finally the validity of this integral equation has the following two implications X t x f s x s ds x 0 X x lim ff s x s ds x f lim f s x s ds x f f s lim x s ds x ff s x s ds Thus the function rx 1 satisfying the integral equation x 1 x f s x s ds for all 1 18 b t b dx 0 ff s x s ds 1 X 1 dt This now proves that the curve X to 8 4 82 thus obtained is a solution of the initial value problem