Question Number 60203 by meme last updated on 18/May/19 $${demonstrate}\: \\ $$$$\mid{sin}\left({y}\right)−{sin}\left({x}\right)\mid\leqslant\mid{y}−{x}\mid \\ $$ Commented by Mr X pcx last updated on 19/May/19 $${let}\:{f}\left({x}\right)={sinx}\:{we}\:{have}\:{f}^{,} \left({x}\right)={cosx}…
Question Number 125739 by ZiYangLee last updated on 13/Dec/20 $$\mathrm{Given}\:\mathrm{that}\:{x}^{{x}^{\mathrm{4}} } =\mathrm{4},\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}^{{x}^{\mathrm{2}} } +{x}^{{x}^{\mathrm{8}} } . \\ $$ Commented by Dwaipayan Shikari last…
Question Number 60202 by meme last updated on 18/May/19 $${construct}\:{the}\:{point}\:{M}^{'} =\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\left({z}+\mid{z}\mid\right)}{\mathrm{2}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 191275 by Mingma last updated on 22/Apr/23 Answered by mr W last updated on 22/Apr/23 Commented by mr W last updated on 22/Apr/23…
Question Number 125736 by snipers237 last updated on 13/Dec/20 $${P}_{{o}} =\mathrm{1}\:\:,{P}_{\mathrm{1}} =\mathrm{1}+{X}\:{and}\:{for}\:{all}\:{n}\geqslant\mathrm{1} \\ $$$${P}_{{n}+\mathrm{1}} ={P}_{{n}} +{XP}_{{n}−\mathrm{1}} \: \\ $$$${Explicit}\:\:{P}_{{n}} \:\:{and}\:{prove}\:{that}\:{its}\:{roots}\:{are}\:{all}\:{real}. \\ $$ Terms of Service…
Question Number 191274 by Mingma last updated on 22/Apr/23 Commented by mr W last updated on 22/Apr/23 $${it}\:{can}\:{be}\:{proved}\:{that} \\ $$$${radius}\:{of}\:{red}\:{circle}\:{R}={blue}\:{length}\:{l} \\ $$$$\Rightarrow\:{area}\:{of}\:{red}\:{circle}\:=\pi{l}^{\mathrm{2}} \\ $$ Commented…
Question Number 125737 by snipers237 last updated on 13/Dec/20 $$\:{Find}\:{C}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+{e}^{−{u}} }\:{du} \\ $$$${Prove}\:{that}\:\int_{\mathrm{1}} ^{\mathrm{1}+\frac{\mathrm{1}}{{n}}} \sqrt{\mathrm{1}+{x}^{{n}} }\:{dx}\:\underset{\infty} {\sim}\:\frac{{C}}{{n}}\: \\ $$ Answered by MJS_new last…
Question Number 60198 by Mr X pcx last updated on 18/May/19 $${find}\:{lim}_{{n}\rightarrow+\infty} \:{ln}\left(\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}+\frac{{k}^{\mathrm{4}} }{{n}^{\mathrm{4}} }\right)^{\frac{\mathrm{1}}{{n}}} \right) \\ $$ Answered by tanmay last updated…
Question Number 60197 by Mr X pcx last updated on 18/May/19 $${valculste}\:{lim}_{{n}\rightarrow+\infty} \left({ln}\left(\left(\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}+\frac{{k}^{\mathrm{3}} }{{n}^{\mathrm{3}} }\right)\right)^{\frac{\mathrm{1}}{{n}}} \right)\right. \\ $$ Commented by Mr X pcx…
Question Number 125728 by Mammadli last updated on 13/Dec/20 $$\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{{lim}}}\left(\mathrm{1}+\frac{\mathrm{3}}{\boldsymbol{{n}}\left(\boldsymbol{{n}}+\mathrm{3}\right)}\right)^{\boldsymbol{{n}}^{\mathrm{2}} } =? \\ $$ Answered by bramlexs22 last updated on 13/Dec/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left[\left(\mathrm{1}+\frac{\mathrm{3}}{{n}^{\mathrm{2}} +\mathrm{3}{n}}\right)^{\frac{{n}^{\mathrm{2}}…