一些常用函数及其泰勒(Taylor)展开式的图像

图1)exp(xy及其Taylor展开式其中，。!4!3!21)(;!3!21)(;!21)(;1)(;)exp(43244323322211xxxxxPyxxxxPyxxxPyxxPyexyx-3-2-10123-50510152025Figure1y=exp(x)anditsTaylorexpansionequationXYyy1y2y3y4图2)sin(xy及其Taylor展开式其中，。!7!5!3)(;!5!3)(;!3)(;)();sin(75377535533311xxxxxPyxxxxPyxxxPyxxPyxy-4-3-2-101234-8-6-4-202468Figure2y=sin(x)anditsTaylorexpansionequationXYyy1y3y5y7图3)cos(xy及其Taylor展开式其中，。!8!6!4!21)(;!6!4!21)(;!4!21)(;!21)();cos(864288642664244222xxxxxPyxxxxPyxxxPyxxPyxy-4-3-2-101234-8-6-4-2024Figure3y=cos(x)anditsTaylorexpansionequationXYyy2y4y6y8图4)1ln(xy及其Taylor展开式其中，。432)(;32)(;2)(;)();1ln(43244323322211xxxxxPyxxxxPyxxxPyxxPyxy-1-0.500.511.52-3-2-10123Figure4y=ln(x)anditsTaylorexpansionequationXYyy1y2y3y4图5)sh(xy及其Taylor展开式其中，。!7!5!3)(;!5!3)(;!3)(;)(;2)sh(75377535533311xxxxxPyxxxxPyxxxPyxxPyeexyxx-5-4-3-2-1012345-80-60-40-20020406080Figure5y=sh(x)anditsTaylorexpansionequationXYyy1y3y5y7图6)ch(xy及其Taylor展开式其中，。!8!6!4!21)(;!6!4!21)(;!4!21)(;!21)(;2)ch(864288642664244222xxxxxPyxxxxPyxxxPyxxPyeexyxx-5-4-3-2-101234501020304050607080Figure6y=ch(x)anditsTaylorexpansionequationXYyy2y4y6y8图7)1(xy及其Taylor展开式其中，。43244323322211!4)3)(2)(1(!3)2)(1(!2)1(1)(;!3)2)(1(!2)1(1)(;!2)1(1)(;1)(;)1(xxxxxPyxxxxPyxxxPyxxPyxy-1-0.8-0.6-0.4-0.200.20.40.60.81-2024681012141618Figure7.1y=(1+x)aanditsTaylorexpansionequation(a=-1.5)XYyy1y2y3y4-1-0.8-0.6-0.4-0.200.20.40.60.810.20.40.60.811.21.41.6Figure7.2y=(1+x)aanditsTaylorexpansionequation(a=0.5)XYyy1y2y3y4-1-0.8-0.6-0.4-0.200.20.40.60.81-1001020304050Figure7.3y=(1+x)aanditsTaylorexpansionequation(a=5.5)XYyy1y2y3y4