1.lim (x-3) * cot(π/3 * x)
= lim (x-3) / sin(π/3 * x) * lim cos(π/3 * x)
% lim cos(π/3 * x) = -1 %
% 用洛必达法则对 (x-3) / sin(π/3 * x) 的上下求导 %
= -1 * lim 1/(π/3 * cos(π/3 * x))
= 3/π
2.lim xlnx
= lim lnx / (1/x)
% 用洛必达法则对 lnx / (1/x) 的上下求导 %
= lim (1/x) / (-1 / x^2)
= - lim x
= 0