lim(x->无穷)[ln(1+1/x)]/[arc cotx]用洛必达法则求

问题描述:

lim(x->无穷)[ln(1+1/x)]/[arc cotx]用洛必达法则求

lim(x->无穷)[ln(1+1/x)]/[arc cotx]
分子分母同时求导得lim(x->无穷)[ln(1+1/x)]/[arc cotx]
=lim(x->无穷)[[-1/(x^2+x)]/[-1/(1+x^2)] =lim(x->无穷)(1+x^2)/(x^2+x)=1