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求lim(x→0+) ( 2/π*cosπ/2(1-x))/x的极限
人气:233 ℃ 时间:2025-02-21 21:34:51
解答

lim(x→0+) { 2/π*cos[(π/2)(1-x)] } / x
= lim(x→0+) cos (π/2 - πx/2) / (πx/2)
= lim(x→0+) sin (πx/2) / (πx/2)
x→0+ 时 πx/2→0
则 lim(x→0+) sin (πx/2) / (πx/2)=1

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