limx→2(2-X)tanxπ/4的详细解答

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2025-06-27 11:25:40
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回答1:

y=2-x

lim(x->2) (2-x) tan(πx/4)

=lim(y->0)  ytan[π(2-y)/4]

=lim(y->0)  ytan(π/2-πy/4)

=lim(y->0)  y.cot(πy/4)

=lim(y->0)  y/tan(πy/4)

y->0  tan(πy/4) ~ πy/4  等价无穷小

=lim(y->0)  y/(πy/4)

=4/π