1 4 Taylor Series www flax fat parabola in I X b Goal approximate f CH near b by a power series we compute fly dy fix fl b fix f b t ftyldy dd u.ly x integration by parts f 44 Tidy ly x If ly ly Hf hildy recall hyzfjhf.gl g ggtufghgY lx bIf'lbl Slx Hf Holy flxt flh.lt x b f't b tf Ix Hf lyldy linear approximation another integrationbyparts yields check the computation flxt flbltlx h.lt tbh 5 f lb t g f lyldy c Second orderapproximation parabola
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1 4Taylor Serieswww
flax fatparabola
in
I Xb
Goal approximate fCH near b by a powerseries
we compute flydy fix flb
fix f b t ftyldyddu.ly x
integrationbyparts f 44Tidy ly x If ly ly Hf hildy
recallhyzfjhf.gl g
ggtufghgYlx bIf'lbl Slx Hf Holy
flxt flh.lt x b f'tb tfIx Hf lyldylinearapproximation