limx→0 arctanx/x
令t=arctanx
原式=limt→0 t/tant
=limt→0 tcost/sint
=1
limx→无穷[ (4+3x)/(3x-1)]^(x+1)
=limx→无穷[ (1+5/(3x-1))]^(x+1)
=limx→无穷[ (1+5/(3x-1))]^[(3x-1)/5*5(x+1)/(3x-1)]
=limx→无穷[ (1+5/(3x-1))]^(3x-1)/5]^lim(x->∞)[5(x+1)/(3x-1)]
=e^(5/3)
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