lim[sin(x2-1)/x-1] x趋近于1 等于什么

lim[sin(x2-1)/x-1] x趋近于1 等于什么
lim[sin(x2-1)/x-1] x趋近于1 等于什么

lim[sin(x2-1)/x-1] x趋近于1 等于什么
lim(x->1)[sin(x^2-1)/x-1]=
lim(x->1)[(x^2-1)/x-1]=
lim(x->1)(x+1)=2.

原式=lim(x->1){[sin(x²-1)/(x²-1)]*[(x²-1)/(x-1)]}
=lim(x->1){[sin(x²-1)/(x²-1)]*(x+1)}
=lim(x->1){[sin(x²-1)/(x²-1)]*lim(x->1)(x+1)
=1*(1+1) (应用重要极限lim(z->0)(sinz/z)=1)
=2。