lim(x→0)lncos2x/lncos3x Using equivalent infinitesimal to calculate

lim(x→0)lncos2x/lncos3x
=lim(x→0)ln(1+cos2x-1)/ln(1+cos3x-1)
=lim(x→0) (cos2x-1)(cos3x-1)
=lim(x→0) (2x)^2/(3x)^2
=4/9

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