lim(根下x方+1_跟下x方-1)求极根

lim(根下x方+1_跟下x方-1)求极根
lim(根下x方+1_跟下x方-1)求极根

lim(根下x方+1_跟下x方-1)求极根
lim[x→∞] √(x²+1)-√(x²-1),进行有理化,上下乘√(x²+1)+√(x²-1)消除分子根号
=lim[x→∞] [√(x²+1)-√(x²-1)][√(x²+1)+√(x²-1)]/[√(x²+1)+√(x²-1)]
=lim[x→∞] [(x²+1)-(x²-1)]/[√(x²+1)+√(x²-1)]
=lim[x→∞] 2/[√(x²+1)+√(x²-1)],分子不变,分母趋向无限大,于是整式趋向零
=2/∞
=0