Question

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Answer 1

Правило Лопиталя:

$limlimits_{x to 0}frac{ln(cos3x)}{ln(cosx)}=limlimits_{x to 0}frac{frac{-3, sin3x}{cos3x}}{frac{-sinx}{cosx}}=limlimits_{x to 0}frac{3, sin3xcdot cosx}{cos3xcdot sinx}=\\=Big [, sin3xsim 3x; ;; sinxsim x; ; pri; ; xto 0, Big ]=\\=limlimits _{x to 0}frac{3cdot 3xcdot cosx}{xcdot cos3x}=limlimits _{x to 0}frac{3cdot 3xcdot 1}{xcdot 1}=frac{9}{1}=9$