求函数极限,x趋于正无穷时,lim[sin(x+1)^(1/2)-sin(x-1)^(1/2)]

∵lim(x->+∞){[√(x+1)-√(x-1)]/2}=lim(x->+∞){[(x+1)-(x-1)]/[2(√(x+1)+√(x-1))]} (分子有理化)=lim(x->+∞){1/[√(x+1)+√(x-1)]}=lim(x->+∞){(1/√x)/[√(1+1/x)+√(1-1/x)]} (分子分母同除√x)=0/[√(1+0)...