Category: Relation and Functions

Question Number 66341 by mathmax by abdo last updated on 12/Aug/19 $$find{lim}_{n\to +\mathrm{\infty }}\frac{1}{n^4}\sum _{k=1}^n\frac{k^3}{\sqrt{{(1+{\left(\frac{k}{n}\right)}^2)}^3}}$$ Commented by Prithwish sen…

Question Number 66322 by mathmax by abdo last updated on 12/Aug/19 $$letf\left(x\right)={\left(cosx\right)}^{\frac{1}{x}}\left(1\right)provethatf\left(x\right)\sim 1-\frac{x}{2}+\frac{x^2}{8}(x\to 0)$$$$\left(2\right)ptovethat{f}^{{}^{\prime }}\left(x\right)\sim -\frac{2}{\pi }{e}^{(\frac{1}{x}-1)ln\left(cosx\right)}(x\to \frac{\pi }{2})$$ Terms of Service Privacy Policy…

Question Number 66318 by mathmax by abdo last updated on 12/Aug/19 $$find{lim}_{x\to 0}{\left(\frac{1+x}{1-x}\right)}^{\frac{1}{sinx}}$$ Commented by mathmax by abdo last updated on 24/Aug/19 $${let}\:{f}\left({x}\right)=\left(\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\right)^{\frac{\mathrm{1}}{{sinx}}}…

Question Number 66316 by mathmax by abdo last updated on 12/Aug/19 $${lim}_{x\to \frac{\pi }{2}}\frac{ln\left({sin}^{2}x\right)}{{(\frac{\pi }{2}-x)}^2}$$$$$$ Commented by mathmax by abdo last…

Question Number 66317 by mathmax by abdo last updated on 12/Aug/19 $$calculate{lim}_{x\to 0}\frac{ln\left(cosx\right)}{1-cos\left(2x\right)}$$ 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}}…