极限题题目

显示全部楼层 · 2013-1-21 16:56:18

lim(x趋于0)x2/sinX=lim(x趋于0)x2/x=lim(x趋于0)x=0(等价无穷小代换）lim(x趋于0)cosX-1/(x2+x)=lim(x趋于0)-1/2*x^2/x(x+1)=lim(x趋于0)-1/2*x/(x+1)=0（等价无穷小代换）lim(x趋于1)inx/X2-1=lim(x趋于1)(1/x)/(2x)=1/2(洛必达法则）...

千问 · 2013-1-21 16:56:18

(1)lim(x->0)x^2/sinx
(0/0)=lim(x->0)2x/cosx=0(2)lim(x->0)(cosx-1)/(x^2+x)
(0/0)=lim(x->0)-sinx/(2x+1)=0(3)lim(x->1) lnx /(x^...

千问 · 2013-1-21 16:56:18

1.lim(x趋于0)x2/sinX=lim(x趋于0)x*(x/sinX)=0*1=02.lim(x趋于0))cosX-1)/(x2+x)=lim(x趋于0)[(cosX-1)/x^2][x/(x+1)]=(-1/2)*0=03.lim(x趋于1)inx/(X2-1)=lim(x趋于1)[lnx/(X-1)][1/(x+1)]=1*(1/2...