Question Number 227426 by Elie last updated on 25/Jan/26 $${Un}\:=\:\frac{\mathrm{5}{n}−\mathrm{3}}{\mathrm{3}{n}−\mathrm{5}} \\ $$$${Un}\:=\:\frac{{n}\left(\mathrm{5}−\frac{\mathrm{3}}{{n}}\right)}{{n}\left(\mathrm{3}−\frac{\mathrm{5}}{{n}}\right)} \\ $$$${Un}\:=\:\frac{\left(\mathrm{5}−\frac{\mathrm{3}}{{n}}\right)}{\left(\mathrm{3}−\frac{\mathrm{5}}{{n}}\right)} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}{Un}\:=\:\frac{\left(\mathrm{5}−\frac{\mathrm{3}}{\infty}\right)}{\left(\mathrm{3}−\frac{\mathrm{5}}{\infty}\right)}=\:\frac{\mathrm{5}}{\mathrm{3}} \\ $$$${Good}\:{Luck} \\ $$ Terms of Service Privacy…
Question Number 227067 by Spillover last updated on 29/Dec/25 Answered by peace2 last updated on 29/Dec/25 $$\frac{\mathrm{1}}{{x}}\rightarrow{y} \\ $$$$=\int_{\mathrm{1}} ^{\infty} \frac{\mathrm{1}}{{y}}.\frac{\left[{y}\right]}{{y}^{\mathrm{2}} }{dy}=\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\int_{{k}} ^{{k}+\mathrm{1}}…
Question Number 227051 by mnjuly1970 last updated on 28/Dec/25 $$ \\ $$$$\:\:\:\:\:\underset{{n}\in\mathbb{N}\cup\left\{\mathrm{0}\right\}} {\sum}{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} +\mathrm{3}{n}\:+\:\mathrm{2}}\:\right)=?\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare\: \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$ Commented by Spillover last updated on…
Question Number 226973 by CrispyXYZ last updated on 23/Dec/25 $$\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:\frac{\mathrm{1}}{{n}}}{{n}+\frac{\mathrm{1}}{\mathrm{1}}}\:+\:\frac{\mathrm{sin}\:\frac{\mathrm{2}}{{n}}}{{n}+\frac{\mathrm{1}}{\mathrm{2}}}\:+\:…\:+\:\frac{\mathrm{sin}\:\frac{{n}}{{n}}}{{n}+\frac{\mathrm{1}}{{n}}}\right)=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 226815 by CrispyXYZ last updated on 16/Dec/25 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{cos}\:\frac{{x}}{\mathrm{2}}\:\mathrm{cos}\:\frac{{x}}{\mathrm{2}^{\mathrm{2}} }\:…\:\mathrm{cos}\:\frac{{x}}{\mathrm{2}^{{n}} }\right)\right)\:=\:? \\ $$ Answered by AgniMath last updated on 16/Dec/25 $${sin}\mathrm{2}\theta\:=\:\mathrm{2}{sin}\theta{cos}\theta \\…
Question Number 226550 by gregori last updated on 03/Dec/25 $$\:\:\:\: {a}+{b}+{c}\:=\:{x}\: \\ $$$$\:\:\:\: \underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} }{{abc}}\:=? \\ $$ Answered by peace2 last updated…
Question Number 224713 by efronzo1 last updated on 28/Sep/25 $$\:\:\:\cancel{\underline{\underbrace{\boldsymbol{{x}}}}} \\ $$ Answered by mehdee7396 last updated on 29/Sep/25 $$\mathrm{1} \\ $$ Commented by gregori…
Question Number 224288 by mnjuly1970 last updated on 31/Aug/25 $$ \\ $$$$\:\:\:\:\:\:\mathrm{P}=\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\prod}}\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\frac{\mathrm{1}}{{k}}}\:\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}{k}}\right)}\:=?\:\:\:\: \\ $$$$ \\ $$ Commented by Frix last updated on 31/Aug/25…
Question Number 223990 by RoseAli last updated on 12/Aug/25 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{x}\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{5}} −\mathrm{32}\:}{{x}−\mathrm{1}} \\ $$ Commented by prathita last updated on 12/Aug/25 $$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}} \\ $$…
Question Number 223193 by Tawa11 last updated on 17/Jul/25 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\mathrm{tan}^{−\:\mathrm{1}} \left(\mathrm{r}\:\mathrm{sin}\:\theta\right)\:\mathrm{d}\theta\:\:\:=\:\:\:\mathrm{2}\boldsymbol{\chi}_{\mathrm{2}} \left(\frac{\sqrt{\mathrm{1}\:\:+\:\:\mathrm{r}^{\mathrm{2}} }\:\:−\:\:\mathrm{1}}{\mathrm{r}}\right) \\ $$ Terms of Service Privacy Policy Contact:…