求极限limx趋于0等于(e^x-x-1)\/3x
lim（e^x-x-1）\/(3x)=lim(e^x-1)\/3(洛必达法则求得)=0
求极限lim(x→0) (e^x-x-1)\/x^3
当x趋于0时，e^x-1可等价于x 上述极限计算过程如下：lim(x->0)(x-x)\/x^3=0
limx→0e^x-x-1\/x求极限
=lim[x-->0](1+x+o(x)-x-1)\/x =lim[x-->0]o(x)\/x =0 注：e^x=1+x+x^2\/2!+x^3\/3!+……=1+x+o(x)
e^xcosx-x-1)\/x^3求极限 lim 趋向于0
如图所示
求极限lim(x→0)(e^x-e^-x)\/sin x
应用极限公式：lim(y->0) (e^y - 1) \/ y = 1 以及 lim(y->0) siny \/ y = 1 lim(x->0) (e^x - e^-x) \/ sinx = lim (e^x - 1\/e^x) \/ sinx = lim (e^2x - 1) \/ (e^x*sinx)= 2 * lim (e^2x - 1) \/ (2x) * x \/ sinx * 1\/e^x = 2 * (1...
limx→0 e^x-1\/ln(1十3x)
2013-01-10 limx趋向于0, x^2\/ln(1-3x)=? 1 2012-03-24 求极限:limx趋向于0 (e)^(x)^2-1\/ln(1+... 2011-09-02 limx->0 ln(1+3x)\/sin4x 1 2011-12-21 求极限 limx趋近于0 (tan3x-3x)\/ln(1+2... 2014-06-19 limx^ln(e^x-1)其中(x-0+) 2011-12-31 limx->∞...
求极限lim(x→0) (e^x-x-1)\/x
lim(x→0) (e^x-x-1)\/x (0\/0)= lim(x→0) (e^x-1)\/1 = 0
lim x->0 (e^3x -1)\/sinx =
Taylor 展开 e^3x=1+3x+o(x)sinx=x+o(x)原式 = limx->0 (3x+o(x))\/(x+o(x))=3 o(x)是相对于x的无穷小,即二阶以上无穷小
求极限lim(x→0) (e^x-x-1)\/x
原式=lim [x→0] [(e^x-1)\/x-1]设e^x-1=t,e^x=1+t,x=ln(1+t),当x→0时,t→0,lim [x→0] [(e^x-1)\/x]=lim [t→0] {t\/[ln(1+t)]=lim [t→0] {1\/[ln(1+t)^(1\/t)]=1\/lne =1\/1 =1,∴原式=lim [x→0] [(e^x-1)\/x-1]=1-1=0....
