极限函数.ppt

极限0极限的概念0极限运算法则0求极限方法举例1、极限的定义0 0lim ( ) ( ) , ( lim 0)x x x xf x A f x A? ?? ?? ????其中无穷小量:是指绝对值不断增大的量的倒数变量y在某个变化过程中以常数A为极限:是指在这个变化过程中变量y可以表示成常数A与无穷小的和的形式0lim 0x x???2、函数极限运算法则),(lim0xfxx?定理4 若)(lim0xgxx?均存在,则1)2))(lim)(lim)]()([lim000xgxfxgxfxxxxxx??????)(lim)(lim)]()([lim000xgxfxgxfxxxxxx??????)(lim)(lim00xfkxkfxxxx???(k为常数)3) 当0)(lim0??xgxx时,).(lim/)(lim)()(lim000xgxfxgxfxxxxxx????????xxxx求解)53(lim22???xxx?5lim3limlim2222??????xxxxx5limlim3)lim(2222??????xxxxx52322????,03??531lim232?????xxxx)53(lim1limlim22232????????3123??3、求极限方法举例解)32(lim21???xxx?,0?商的法则不能用)14(lim1??xx?又,03??1432lim21??????????????????xxxx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?????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)解:原式32372222lim2??????????xxxxx例4 求)1113(lim31????xxx解: 原式11)2(lim)1()1)(2(lim2131??????????????xxxxxxxx又例: 求2237lim2?????xxx3722)22)(22()37)(37(lim2???????????????xxxxxxx)1()1(3lim321??????xxxx)00(型)(型???例5mmmnnnxbxbxbaaxxa????????????????11010lim(a0≠0,b0≠0,m,n>0).解:1)m=n, 原式0010101111limbaxbxbbxaxaannnnx????????????????2)m>n, 原式011lim1010????????????????????mmmnmnmnxxbxbbxaaxxa3)m<n,原式=∞.??????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)