大学文科数学，用洛必达法则求，第九大题第3579和11小题，会的帮一下，帮帮忙

Question

如题所述

Answer 1

=lim(sec²x-1)/(1-cosx)=lim(1+cosx)/cos²x=2
=limxcos2x/sin2x=lim(cos2x-2xsin2x)/2cos2x=1/2
=lim(e^(1/x)-1)/(1/x)=lime^(1/x)(1/x)'/(1/x)'=lime^(1/x)=1
=lim(xlnx-(x-1))/(x-1)lnx=lim(lnx+1-1)/(lnx+(x-1)/x)=limxlnx/(xlnx+x-1)=lim(lnx+1)/(lnx+1+1)=1/2
=lime^(tanxln(1/x))=e^limln(1/x)/cotx=e^lim((-1/x²)/(1/x))/-ccs²x=e^limsin²x/x=e^lim2sinxcosx=e^0=1