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Question Number 59542 by Mikael_Marshall last updated on 11/May/19

$$\underset{x\to 0}{lim}\frac{\ln \left(\mathrm{cosx}\right)}{{\mathrm{x}}^2}$$$$Ihaveadoubt$$

Commented by kaivan.ahmadi last updated on 11/May/19

$$hop$$$${lim}_{x\to 0}\frac{-sinx}{2xcosx}={lim}_{x\to 0}\frac{-tgx}{2x}=$$$${lim}_{x\to 0}\frac{-(1+{tg}^{2}x)}{2}=\frac{-1}{2}$$

Commented by Mikael_Marshall last updated on 11/May/19

$$ohthankyouSir$$

Commented by maxmathsup by imad last updated on 11/May/19

$$cosx\sim 1-\frac{x^2}{2}andln(1-\frac{x^2}{2})\sim -\frac{x^2}{2}\Rightarrow \frac{ln\left(cosx\right)}{x^2}\sim -\frac{1}{2}\Rightarrow$$$${lim}_{x\to 0}\frac{ln\left(cosx\right)}{x^2}=-\frac{1}{2}$$

Commented by Mikael_Marshall last updated on 11/May/19

$$thankyouSir$$

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