lim(x→0)lncos2x/lncos3x
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lim(x→0)lncos2x/lncos3x
用等价无穷小量求
用等价无穷小量求
![lim(x→0)lncos2x/lncos3x](/uploads/image/z/5134664-56-4.jpg?t=lim%28x%E2%86%920%29lncos2x%2Flncos3x)
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
=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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