Category: Limits

Question Number 187495 by mathlove last updated on 18/Feb/23 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 121878 by oustmuchiya@gmail.com last updated on 12/Nov/20 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 121822 by liberty last updated on 12/Nov/20 $$\underset{x\to 0}{\lim }\frac{\sqrt{2-2\cos 2\mathrm{x}}}{3\mid \sin 4\mathrm{x}\mid }=?$$ Answered by bemath last updated on 12/Nov/20 $$\begin{cases}{\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2}−\mathrm{2}\left(\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} {x}\right)}}{\mathrm{3}\mid\mathrm{sin}\:\mathrm{4}{x}\mid}\:=\:\underset{{x}\rightarrow\mathrm{0}^{+} }…

Question Number 121728 by oustmuchiya@gmail.com last updated on 11/Nov/20 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 121727 by oustmuchiya@gmail.com last updated on 11/Nov/20 Answered by TANMAY PANACEA last updated on 11/Nov/20 $$1)b^2=\frac{a+1}{2}\to 2b\times \frac{db}{da}=\frac{1}{2}whena=4b=\sqrt{\frac{5}{2}}$$$$gradint{\left(\frac{db}{da}\right)}_{a=4}={\left(\frac{1}{4b}\right)}_{b=\sqrt{\frac{5}{2}}}=\frac{\sqrt{2}}{4\times \sqrt{5}}$$$$\left.{ii}\right)\frac{{dt}}{{dx}}=\frac{{x}×\mathrm{2}{x}−\left({x}^{\mathrm{2}}…