求解lim(x->1) (2x/(x+1))^(2x/(x+1))答案是(5/2)^(5/2)吗?说是用特殊极限求解,我也导不成x_数学解答

求解lim(x->1) (2x/(x+1))^(2x/(x+1))
答案是(5/2)^(5/2)吗?说是用特殊极限求解,我也导不成x趋于无穷大时lim(1+1/x)^x=e的形式啊?还望赐教

人气：335 ℃　时间：2020-10-02 05:37:42

解答

lim(x->1) (2x/(x+1))^(2x/(x+1))
=lim(x->1) e^ln(2x/(x+1))^(2x/(x+1))
=lim(x->1) e^(2x/(x+1))ln(2x/(x+1))
=1 [lim(x->1) (2x/(x+1))ln(2x/(x+1))=0,e为常数]