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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
1年前
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