Category: Limits

Question Number 105114 by john santu last updated on 26/Jul/20 $$\underset{x\to 0}{\lim }\frac{2-\sqrt[3]{1-\sin {}^2\left(3x\right)}-\sqrt[3]{1-\sin {}^2\left(2x\right)}}{x^2}$$ Answered by bemath last updated on 26/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}}…

Question Number 105106 by bemath last updated on 26/Jul/20 $$\underset{x\to 0}{\lim }\frac{\sin \left(\pi \cos {}^{2}x\right)}{3x^2}?$$ Answered by bramlex last updated on 26/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\left(\pi\:\mathrm{cos}\:^{\mathrm{2}} {x}\right)}{\mathrm{3}{x}^{\mathrm{2}}…

Question Number 170565 by cortano1 last updated on 27/May/22 Answered by Mathspace last updated on 27/May/22 $${f}^{'} \left({x}\right)={x}^{\mathrm{3}} \frac{\mathrm{2}\left({x}+\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{1}−\mathrm{3}\left({x}+\mathrm{2}\right)^{\mathrm{4}} }−{x}^{\mathrm{3}} \frac{\mathrm{2}\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{1}−\mathrm{3}\left({x}+\mathrm{1}\right)^{\mathrm{4}} } \…

Question Number 170551 by 2407 last updated on 26/May/22 Answered by JDamian last updated on 26/May/22 $$3$$ Answered by Rasheed.Sindhi last updated on…

Question Number 170537 by 2407 last updated on 26/May/22 Commented by cortano1 last updated on 26/May/22 $$\underset{n\to \mathrm{\infty }}{\lim }\sqrt{n}\sqrt{1+\frac{1}{\sqrt{n}}}-\sqrt{n}=$$$$\underset{n\to \mathrm{\infty }}{\lim }\sqrt{n}(\sqrt{1+\frac{1}{\sqrt{n}}}-1)=$$$$=\frac{1}{2}$$…