求函数的极限 lim cosx/(cosx/2-sinx/2) x->π/2

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求函数的极限 lim cosx/(cosx/2-sinx/2) x->π/2
求函数的极限 lim cosx/(cosx/2-sinx/2) x->π/2

求函数的极限 lim cosx/(cosx/2-sinx/2) x->π/2
分子分母求导
-sinx/(-0.5sinx/2-0.5cosx/2)
1/0.5(sinπ/4+cosπ/4)
=根号2

=lim[(cosx/2)^2-(sinx/2)^2]/(cosx/2-sinx/2) x->π/2
=lim(cosx/2+sinx/2) x->π/2
=cosπ/4+sinπ/4
=根号2