求极限 lim→无穷大[(x+1)/(x-1)]^x-1 lim→正无穷[√(x^2+x)-√(x^2-x)]
问题描述：
求极限 lim→无穷大[(x+1)/(x-1)]^x-1 lim→正无穷[√(x^2+x)-√(x^2-x)]
求详解
答
1.此为1^∞型,联想到(1+1/x)^(x)~e,x→∞lim [(x+1)/(x-1)]^(x-1)x→∞=lim [1+2/(x-1)]^(x-1)x→∞=lim [1+2/(x-1)]^{[(x-1)/2]·2}x→∞=e²2.此题需分子有理化：lim √(x²+x)-√(x²-x)x→＋∞=lim ...