Category: Limits

Question Number 69478 by Henri Boucatchou last updated on 24/Sep/19 $$\underset{\mathit{n}\to \mathrm{\infty }}{\mathit{l}\mathit{i}\mathit{m}\mathit{s}\mathit{i}\mathit{n}}\left(\mathit{n}\mathit{\pi }\right)=?$$ Commented by mathmax by abdo last updated on 24/Sep/19 $${sin}\left({n}\pi\right)=\mathrm{0}\:\Rightarrow{lim}_{{n}\rightarrow+\infty} {sin}\left({n}\pi\right)=\mathrm{0}…

Question Number 69338 by Rasheed.Sindhi last updated on 22/Sep/19 Commented by Prithwish sen last updated on 22/Sep/19 $$\mathrm{it}\mathrm{is}\mathrm{the}\mathrm{series}\mathrm{of}$$$$1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\dots \dots$$$$\mathrm{tan}^{−\mathrm{1}} \mathrm{x}=\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{3}}+\frac{\mathrm{x}^{\mathrm{5}} }{\mathrm{5}}−\frac{\mathrm{x}^{\mathrm{7}}…

Question Number 134858 by mnjuly1970 last updated on 07/Mar/21 Answered by mathmax by abdo last updated on 07/Mar/21 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)={\mathrm{lnxln}}^2(1-\mathrm{x})\mathrm{changement}1-\mathrm{x}=\mathrm{t}\mathrm{give}\mathrm{x}=1-\mathrm{t}(\mathrm{t}\to 0^{+})$$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{ln}\left(\mathrm{1}−\mathrm{t}\right)\mathrm{ln}^{\mathrm{2}} \left(\mathrm{t}\right)\:=\mathrm{g}\left(\mathrm{t}\right)\:\mathrm{we}\:\mathrm{have} \…

Question Number 69255 by TawaTawa last updated on 21/Sep/19 $$\underset{x\to 2}{\lim }\sqrt{\frac{{\mathrm{x}}^3-4}{{\mathrm{x}}^2-3\mathrm{x}+2}}$$ Answered by Henri Boucatchou last updated on 21/Sep/19 $$\underset{\boldsymbol{{x}}\rightarrow\mathrm{2}} {\boldsymbol{{lim}}}\sqrt{\frac{\boldsymbol{{x}}^{\mathrm{3}}…

Question Number 69212 by aliesam last updated on 21/Sep/19 $$uselimitcomparisontesttodetermine$$$$theseriesconvergeordiverge$$$$\underset{k=1}{\sum ^{\mathrm{\infty }}}ln(1+\frac{1}{k^2})$$ Answered by mind is power last…