问几道高数极限丫!1.lim x[根号(x^2-1) -x]x->∞2.lim sin6x/sin8xx->03.lim

(1)=lim(x->∞) -x/[根号(x^2-1)+x]
=lim(x->∞) -1/[根号(1-1/x^2)+1]= -1/2;
(2)=lim(x->∞) (sin6x/6x)*6x/[(sin8x/8x)*8x]
=lim(x->0) (6/8)*(sin6x/6x)/(sin8x/8x)=3/4;
(3)=lim(x->0) sinx/(2xcosx)+(3/2)*(sinx/x)
=lim(x->0)[(1/2cosx)+3/2]*(sinx/x)=[1/2+3/2]=2;
(4)=lim(x->π) sin(π-x)/(π-x)
=lim(y->0) siny/y=1;
(5)=lim(x->0)(2-sinx/x)/(1+sinx/x)=2/1=2;
(6)lim(x->0) (1+5x)^[(1/(5x))*5]
=lim(x->0) [(1+5x)^(1/(5x))]^5
=e^5;
(7)=lim(x->0) xcosx/(2sinxcosx)
=lim(x->0) (1/2)*(x/sinx)=1/2