Category: Limits

Question Number 185209 by Rupesh123 last updated on 18/Jan/23 Answered by som(math1967) last updated on 18/Jan/23 $$a)\underset{n\to \mathrm{\infty }}{lim}\frac{1}{n}[{\left(\frac{1}{n}\right)}^{2022}+{\left(\frac{2}{n}\right)}^{2022}+\dots {\left(\frac{n}{n}\right)}^{2022}]$$$$\underset{{n}\rightarrow\infty} {{lim}}\:\frac{\mathrm{1}}{{n}}\underset{{r}=\mathrm{1}} {\overset{{n}}…

Question Number 119629 by 9764954060 last updated on 25/Oct/20 Answered by TANMAY PANACEA last updated on 25/Oct/20 $${ax}^2+bx+c=0$$$$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$$${so}\:{here}\:{x}=\frac{−\mathrm{3}\pm\sqrt{\mathrm{3}^{\mathrm{2}} −\mathrm{4}×\mathrm{2}×\mathrm{7}}}{\mathrm{2}×\mathrm{2}}=\frac{−\mathrm{3}\pm\sqrt{−\mathrm{47}}}{\mathrm{4}}…

Question Number 119517 by bemath last updated on 25/Oct/20 $$\underset{x\to \mathrm{\infty }}{\lim }[\sin (x+\frac{1}{x})-\sin x]=?$$ Answered by Dwaipayan Shikari last updated on 25/Oct/20 $$\underset{x\to \mathrm{\infty }}{\lim }(sin(x+\frac{1}{x})-sinx)$$$$=\underset{{x}\rightarrow\infty}…

Question Number 184960 by mathlove last updated on 14/Jan/23 Answered by cortano1 last updated on 15/Jan/23 $$L=-\frac{9}{4}(\ln 4-1)$$ Commented by mathlove last updated on…

Question Number 184901 by mathlove last updated on 13/Jan/23 $$\underset{\frac{2}{x}\to 2}{\lim }\frac{100+x}{101x}$$ Commented by SEKRET last updated on 13/Jan/23 $$\mathbf{x}\to 1$$ Answered by…