---- **目次 ---- -[[y = arctan x>#arctan]] -[[y = e>#exp]]&sup(){&color(#106096){x}} &color(#106096){x} -[[y = sin x>#sin]] -[[y = cos x>#cos]] -[[y = (1+x)>#sqrt]]&sup(){1/2} -[[y = log x>#log]] &aname(arctan) ---- **y = arctan x の x=0 におけるTaylor展開の状況 ---- #ref(arctan.gif) y = arctan x (黒), y = x (紫), y = x - x3/3 (赤), y = x - x3/3 + x5/5(青), y = x - x3/3 + x5/5 - x7/7(緑). &aname(exp) ---- **y = e&sup(){x} の x=0 におけるTaylor展開の状況 ---- #ref(exp.gif) y = e x (黒), y = 1 + x (紫), y = 1 + x + x2/2 (赤), y = 1 + x + x2/2 + x3/6(青), y = 1 + x + x2/2 + x3/6 + x4/24(緑). ---------------------------------------------------------------------------- &aname(sin) ---- y = sin x の x=0 におけるTaylor展開の状況 ---- y = sin x (黒), y = x (紫), y = x - x3/6 (赤), y = x - x3/6 + x5/120(青), y = x - x3/6 + x5/120 - x7/5040(緑). -------------------------------------------------------------------------------- &aname(cos) ---- y = cos x の x=0 におけるTaylor展開の状況 ---- y = cos x (黒), y = 1 (紫), y = 1 - x2/2 (赤), y = 1 - x2/2 + x4/24 (青), y = 1 - x2/2 + x4/24 - x6/720 (緑). -------------------------------------------------------------------------------- &aname(sqrt) ---- y = (1+x)&sup(){1/2} の x=0 におけるTaylor展開の状況 ---- y = (1+x)1/2 (黒), y = 1 + x/2 (紫), y = 1 + x/2 - x2/8 (赤), y = 1 + x/2 - x2/8 + x3/16(青), y = 1 + x/2 - x2/8 + x3/16 - 5x4/128(緑). -------------------------------------------------------------------------------- &aname(log) ---- y = log x の x=1 におけるTaylor展開の状況 ---- y = log x (黒), y = x-1 (紫), y = (x-1) - (x-1)2/2 (赤), y = (x-1) - (x-1)2/2 + (x-1)3/3 (青), y = (x-1) - (x-1)2/2 + (x-1)3/3 - (x-1)4/4 (緑). ---- #right{by KOYAMA Yoshitaka} #center(){&b(){y=arcsin x} (&color(red){赤}), &space(3) &b(){y=arccos x} (&color(blue){青}) } &aname(arctan) ---- **arctan のグラフと主な値の表 ---- #center(){&b(){y=arctan x} (&color(red){赤}), &space(3) &b(){y=±π/2} (&color(blue){青}) }