x趋近正无穷 ((x^2-2x+1)/(x^2-4x+2))^x 的极限是

题目

x趋近正无穷 ((x^2-2x+1)/(x^2-4x+2))^x 的极限是
如题

答案

y = [(x^2 - 2x + 1)/(x^2 - 4x + 2)]^xlny = x * [2ln(x-1)-ln(x^2-4x+2)] =[2ln(x-1)-ln(x^2-4x+2)]/x^-1因为 lny 的极限属于 0 * ∞ 型,所以应用罗必塔法则,有：lim(lny) = lim[2/(x-1) - 2(x-2)/(x^2-4x+2)]/(-x...