x趋近于-1,用洛必达法求,lim(1-x)^cox(πx/2)
问题描述：
x趋近于-1,用洛必达法求,lim(1-x)^cox(πx/2)
答
lim(x->1) (1-x)^cos(πx/2)=lim(x->1) e^[cos(πx/2)ln(1-x)]=e^ {lim(x->1) [ln(1-x)/sec(πx/2)]}=e^ {lim(x->1) [2cos^2(πx/2)/π(x-1)sin(πx/2)]=e^ {1/π*lim(x->1) [(1+cos(πx))/(x-1)sin(πx/2)]}=e^ {li...