基本初等函數(shù)公式

1、基本初等函數(shù)1常數(shù)函數(shù)：；；cy?1y?ye?2冪函數(shù)：；；；；yx??2xy?xy?1yx??mnnmyxx??3指數(shù)函數(shù)：；xay?xey?4對數(shù)函數(shù)：；；；xyalog?xyln?xy2log?lgyx?5三角函數(shù)：；xysin?xycos?三角函數(shù)是有界函數(shù)，奇函數(shù)；偶函數(shù)sinxcosx6奇函數(shù)：圖形關(guān)于坐標原點對稱；()()fxfx???偶函數(shù)：圖形關(guān)于軸對稱；()()fxfx??y含有因子的是偶函數(shù)；含有因子的是奇函數(shù)，x

2、xaa??xxaa??兩個重要極限1e和1sinlim0??xxxexxx??????????11lim無窮小量有界量＝無窮小量當時，是無窮小量x??1sinnx?1sinlim0??xxx??exxx???101lim極限運算法則：gfgflimlim)lim(???sinlim0xxx???0limsin0xxx??；fkkflim)lim(?limlimlimfgfg??微分公式dxydy??kdxdkx?dxaxdxxdxaaa

3、1)(????adxadxadaxxxln)(???dxdxxxd2)2(2???221log(log)ln2dxxdxdxx???xdxdxxxdcos)(sinsin???dxedxedexxx???)(dxxdxxxd1)(lnln???xdxdxxxdsin)(coscos????導數(shù)公式0)(??c1)(??xaxxaln1)(log??xxcos)(sin??0)0(??2()2xx??xx1)(ln??xxsin)(cos

4、?????01??211xx?????????aaaxxln)(??)()()(??????gfgf)()()(?????gfgffg)()(???fkkf1)(???aaaxxxx21)(??xxee??)(2)()(ggfgfgf?????????????定積分公式()()|()()bbaafxdxFxFbFa????()bbbaaafgdxfdxgdx??????（為常數(shù)）bbaakfdxkfdx???|bbbaaafgdxfgf

5、gdx????????????????????aaa為為為為為x為為fxfxfdxxf為為為為為x為為fxfxfdxxf0)()()()(2)()()(0)(逆矩陣求法用初等行變換求逆矩陣的方法：????1||PIIP?????初等行變換－齊次方程有非零解和零解條件0mnAX??當時齊次方程只有零解。()rAn?0AX?當時齊次方程有非零解。()rAn?0AX?結(jié)論：齊次方程一定有零解。非齊次方程有解（唯一解、無窮多解）、無解的條件mn