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Question Number 66317 by mathmax by abdo last updated on 12/Aug/19
$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{ln}\left({cosx}\right)}{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)} \\ $$
Commented by kaivan.ahmadi last updated on 12/Aug/19
$$\equiv{lim}_{{x}\rightarrow\mathrm{0}} \frac{{ln}\left({cosx}\right)}{\mathrm{2}{x}^{\mathrm{2}} }\overset{{hop}} {=}{lim}_{{x}\rightarrow\mathrm{0}} \frac{−{sinx}}{\mathrm{4}{xcosx}}\overset{{hop}} {=} \\ $$$${lim}_{{x}\rightarrow\mathrm{0}} \:\frac{−{cosx}}{\mathrm{4}{cosx}−\mathrm{4}{xsinx}}=\frac{−\mathrm{1}}{\mathrm{4}} \\ $$
Commented by mathmax by abdo last updated on 12/Aug/19
$${thanks}\:{sir}. \\ $$