lim(x→+π/2) ln(x-π/2)/tanx

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lim(x→+π/2)ln(x-π/2)/tanxlim(x→+π/2)ln(x-π/2)/tanxlim(x→+π/2)ln(x-π/2)/tanxt→+0,int/tan(t+π/2),sin^2

lim(x→+π/2) ln(x-π/2)/tanx
lim(x→+π/2) ln(x-π/2)/tanx

lim(x→+π/2) ln(x-π/2)/tanx
t→+0,int/tan(t+π/2),sin^2(t)/t,t用洛必达一次,等价无穷小一次,结果为0

tanx等价于x,则lim(x→+π/2) ln(x-π/2)/x
用洛必达法则,lim(x→+π/2)(x-π/2)/1
当x→x-π/2时,结果为0
关键是等价无穷小与洛必达法则