文档介绍：第五节极限运算法则?一、极限运算法则?二、求极限方法举例?三、小结思考题一、,)()(lim)3(;)]()(lim[)2(;)]()(lim[)1(,)(lim,)(lim??????????BBAxgxfBAxgxfBAxgxfBxgAxf其中则设证.)(lim,)(limBxgAxf???.0,0.)(,)(???????????其中BxgAxf由无穷小运算法则,得)()]()([BAxgxf???????.0?.)1(成立?)()]()([BAxgxf???ABBA??????))((???????)(?.)2(成立?BAxgxf?)()(BABA??????)(??????????AB?,0,0???B?又,0???,00时当????xx,2B????????BBBB21??B21?推论1).(lim)](lim[,,)(limxfcxcfcxf?则为常数而存在如果常数因子可以提到极限记号外面..)]([lim)](lim[,,)(limnnxfxfnxf?则是正整数而存在如果推论2,21)(2BBB????,2)(12BBB???故有界,.)3(成立?二、????xxxx求解)53(lim22???xxx?5lim3limlim2222??????xxxxx5limlim3)lim(2222??????xxxxx52322????,03??531lim232?????xxxx)53(lim1limlim22232????????3123??小结:则有设,)(.1110nnnaxaxaxf??????nnxxnxxxxaxaxaxf?????????110)lim()lim()(lim000nnnaxaxa??????10100).(0xf?则有且设,0)(,)()()(.20??xQxQxPxf)(lim)(lim)(lim000xQxPxfxxxxxx????)()(00xQxP?).(0xf?.,0)(0则商的法则不能应用若?xQ解)32(lim21???xxx?,0?商的法则不能用)14(lim1??xx?又,03??1432lim21???????由无穷小与无穷大的关系,??????????????xxxx求.,,1分母的极限都是零分子时??x)1)(3()1)(1(lim321lim1221??????????xxxxxxxxx31lim1?????)00(型(消去零因子法)??????xxxxx求解.,,分母的极限都是无穷大分子时??x)(型??.,,3再求极限分出无穷小去除分子分母先用x332323147532lim147532limxxxxxxxxxx?????????????.72?(无穷小因子分出法)小结:为非负整数时有和当nmba,0,000??????????????????????????,,,,0,,lim00110110mnmnmnbabxbxbaxaxannnmmmx当当当??无穷小分出法:以分母中自变量的最高次幂除分子,分母,以分出无穷小,然后再求极限.