比大小

guanmo1

kuing

x 很小时 `\sin x\approx x-x^3/6`
平方得 `\sin^2x\approx x^2-x^4/3`
以及 `\sin(x^2)\approx x^2-x^6/6`
所以前者小。

hbghlyj

import graph;

unitsize(4cm,8cm);
real f1(real x) { return sin(x)^2; }
real f2(real x) { return sin(x^2); }

draw(graph(f1, 0, 1), red,"$\sin^2(x)$");
draw(graph(f2, 0, 1), blue,"$\sin(x^2)$");

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks(trailingzero));
add(legend(),(1.5,.4));