L=lim(x->0) (cosx/cos2x)^[1/(sinx.sin2x) ]
lnL
=lim(x->0) ln[(cosx/cos2x)]/(sinx.sin2x)
=lim(x->0) ln[(cosx/cos2x)]/(2x^2) (0/0 分子分母分别求导)
=lim(x->0) [ -sinx/cosx + 2sin2x/cos2x ]/(4x)
=lim(x->0) (-tanx + 2tan2x )/(4x)
=lim(x->0) [-x + 2(2x) ]/(4x)
=3/4
L = e^(3/4)
=>
lim(x->0) (cosx/cos2x)^[1/(sinx.sin2x) ] = e^(3/4)
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