求一道求极限的高数题,lim（x趋近于无穷）[(x+1)/（x-1）]∧x

题目

求一道求极限的高数题,lim（x趋近于无穷）[(x+1)/（x-1）]∧x

答案

lim(x→∞)[(x+1)/(x-1)]^x
=lim(x→∞){[1+2/(x-1)]^[(x-1)/2]}^2*[1+2/(x-1)]
=lim(t→∞)(1+1/t)^2t,其中t=(x-1)/2
=e^2