Category: Limits

Question Number 118040 by mathocean1 last updated on 14/Oct/20 Answered by Ar Brandon last updated on 14/Oct/20 $$\underset{x\to \frac{\pi }{3}}{\lim }\frac{1-2\cos x}{\pi -3x}=\frac{0}{0}=\underset{x\to \frac{\pi }{3}}{\lim }\frac{2\sin x}{-3}=2\times \frac{\sqrt{3}}{2}\mathbf{÷}-3=-\frac{1}{\sqrt{3}}$$ Answered by bobhans…

Question Number 183483 by cortano1 last updated on 26/Dec/22 $$\underset{x\to 0^{+}}{\lim }\frac{1-\cos \sqrt{x}}{\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x-\dots }}}}}=?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 183376 by TUN last updated on 25/Dec/22 Commented by CElcedricjunior last updated on 25/Dec/22 $$\underset{\mathit{n}=1}{\sum ^{\mathrm{\infty }}}{\mathit{n}\mathit{x}}^{\mathit{n}}=\mathit{x}+2{\mathit{x}}^2+3{\mathit{x}}^3+\dots \mathrm{\infty }{\mathit{x}}^{\mathrm{\infty }}$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\boldsymbol{{x}}\left(\mathrm{1}+\mathrm{2}\boldsymbol{{x}}+\mathrm{3}\boldsymbol{{x}}^{\mathrm{2}} +….+\infty\boldsymbol{{x}}^{\infty−\mathrm{1}}…

Question Number 183269 by TUN last updated on 24/Dec/22 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 117687 by bemath last updated on 13/Oct/20 $$\underset{x\to 0}{\lim }\frac{{(\ln \left(\cosh \mathrm{x}\right)-\ln \left(\cos \mathrm{x}\right))}^2}{\sqrt{\cosh \mathrm{x}}+\sqrt{\cos \mathrm{x}}-2}=?$$ Answered by 1549442205PVT last updated on 13/Oct/20 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}\:}\frac{\left(\mathrm{ln}\:\left(\mathrm{cosh}\:\mathrm{x}\right)−\mathrm{ln}\:\left(\mathrm{cos}\:\mathrm{x}\right)\right)^{\mathrm{2}} }{\:\sqrt{\mathrm{cosh}\:\mathrm{x}}+\sqrt{\mathrm{cos}\:\mathrm{x}}−\mathrm{2}}\:=^{\frac{\mathrm{0}}{\mathrm{0}}} \…