manthanein 发表于 2015-12-31 16:50:08

\(x^{2}+y^{2}\lt r^{2}+2(ax+by)-(a^{2}+b^{2})\)
\((a^{2}+b^{2})(x^{2}+y^{2})\lt (a^{2}+b^{2})r^{2}+2(a^{2}+b^{2})(ax+by)-(a^{2}+b^{2})^{2}\)
\((a^{2}+b^{2})(x^{2}+y^{2})\lt (a^{2}+b^{2})(r^{2}-a^{2}-b^{2})+2(a^{2}+b^{2})(ax+by)\)

manthanein 发表于 2015-12-31 16:57:34

\((ax+by)^{2}-2(a^{2}+b^{2})(ax+by)\lt (a^{2}+b^{2})(r^{2}-a^{2}-b^{2})-(ay-bx)^{2}\)
\((ax+by)^{2}-2(a^{2}+b^{2})(ax+by)+(a^{2}+b^{2})^{2}\lt (a^{2}+b^{2})r^{2}-(ay-bx)^{2}\)
\((ax+by-a^{2}-b^{2})^{2}\lt (a^{2}+b^{2})r^{2}-(ay-bx)^{2}\)

TSC999 发表于 2016-1-1 08:55:43


r2+(a2+b2)+2a2+b2−−−−−−√r>(x−a)2+(y−b)2
(a2+b2−−−−−−√+r)2>(x−a)2+(y−b)2

gxqcn 发表于 2016-1-4 08:22:33

论坛已自带 \(\rm\LaTeX\) 预览功能，在发帖回帖提交之前可先预览效果，平时也可利用该功能练习，没必要专门开贴试验练习。

manthanein 发表于 2016-5-2 21:36:19

本帖最后由 manthanein 于 2016-5-2 21:47 编辑

给定曲线\(F(x,y)=0\)
在曲线上有一点\((x_0,y_0)\),\(F(x_0,y_0)=0\)
另外有一点\((p,q)\)，\(F(p,q)=0\)
有一条过点\((x_0,y_0)\)的直线\(xcos\alpha+ysin\alpha-P=0\)，\(x_0cos\alpha+y_0sin\alpha-P=0\)

manthanein 发表于 2016-5-2 21:40:17

本帖最后由 manthanein 于 2016-5-2 21:46 编辑

\(\displaystyle \lim_{\sqrt{(p-x_0)^2+(q-y_0)^2} \to 0} (pcos\alpha+qsin\alpha-P)=0\)

manthanein 发表于 2016-5-2 21:48:21

本帖最后由 manthanein 于 2016-5-2 22:18 编辑

\(\displaystyle \lim_{(p-x_0)^2+(q-y_0)^2 \to 0} (pcos\alpha+qsin\alpha-P)=0\)
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查看完整版本: 这里允许练习latex吧