当X趋向π/4时,(sinx+cosx)/cos2x的极限

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当X趋向π/4时,(sinx+cosx)/cos2x的极限当X趋向π/4时,(sinx+cosx)/cos2x的极限当X趋向π/4时,(sinx+cosx)/cos2x的极限,(sinx+cosx)/

当X趋向π/4时,(sinx+cosx)/cos2x的极限
当X趋向π/4时,(sinx+cosx)/cos2x的极限

当X趋向π/4时,(sinx+cosx)/cos2x的极限
,(sinx+cosx)/cos2x
=(sinx+cosx)/(cos²x-sin²x)
=(sinx+cosx)/[(cosx+sinx)(cosx-sinx)]
=1/(cosx-sinx)
∴x-->π/4时,1/(cosx-sinx)-->∞
即原式极限不存在
lim(x-->π/4)(sinx+cosx)/cos2x=∞

lim(x->π/4) (sinx+cosx)/cos(2x)
lim(x->π/4) (sinx+cosx) = √2
lim(x->π/4) cos(2x) =0
lim(x->π/4) (sinx+cosx)/cos(2x) 不存在