Question Number 224360 by Tawa11 last updated on 05/Sep/25 Find the equation of the circle which touches the circles x² + y² – 2x +…
Question Number 224233 by Jgrads last updated on 27/Aug/25 $$\mathrm{Prove}\:\mathrm{that}\:\forall\mathrm{n}\geqslant\mathrm{2} \\ $$$$\mathrm{e}^{\mathrm{2n}−\mathrm{1}} −\mathrm{1}\:\geqslant\:\mathrm{2n}\left(\mathrm{2n}−\mathrm{1}\right) \\ $$ Answered by fkwow344 last updated on 27/Aug/25 $$\mathrm{Let}'\mathrm{s}\:{f}\left({x}\right)={e}^{\mathrm{2}{x}−\mathrm{1}} −\mathrm{4}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}…
Question Number 223055 by alcohol last updated on 13/Jul/25 Commented by alcohol last updated on 13/Jul/25 $${please}\:{i}\:{really}\:{really}\:{need}\:{a}\:{detailed} \\ $$$${explanation} \\ $$ Commented by mr W…
Question Number 221413 by BHOOPENDRA last updated on 04/Jun/25 Answered by mr W last updated on 05/Jun/25 $${x}=\mathrm{4}\:\mathrm{cos}\:\theta \\ $$$${y}=\mathrm{2}\:\mathrm{sin}\:\theta \\ $$$${x}+{y}=\mathrm{2}\left(\mathrm{2}\:\mathrm{cos}\:\theta+\mathrm{sin}\:\theta\right)=\mathrm{2}\sqrt{\mathrm{5}}\:\mathrm{sin}\:\left(\theta+\mathrm{tan}^{−\mathrm{1}} \mathrm{2}\right) \\ $$$$\left({x}+{y}\right)_{{min}}…
Question Number 221414 by BHOOPENDRA last updated on 04/Jun/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221154 by gregori last updated on 25/May/25 $$\:{f}\left({x}\right)=\:\frac{{x}}{\mid\:{x}\:\mid\:+\:\mathrm{1}} \\ $$$$\:\:{f}\left({f}\left({f}\left({f}\left({x}\right)\right)\right)\right)\:=? \\ $$ Commented by Frix last updated on 25/May/25 $$\frac{{x}}{\mathrm{4}\mid{x}\mid+\mathrm{1}} \\ $$$${f}_{\mathrm{1}} \left({x}\right)=\frac{{x}}{\mid{x}\mid+\mathrm{1}}…
Question Number 221153 by gregori last updated on 25/May/25 $$\:\:{f}\left({x}\right)=\:\frac{\mathrm{1}}{\mathrm{2}^{{x}} }\:+\:\frac{\mathrm{1}}{\mathrm{3}^{{x}} }\:+\:\frac{\mathrm{1}}{\mathrm{4}^{{x}} }\:+\:…\:+\frac{\mathrm{1}}{\mathrm{4000}^{{x}} } \\ $$$$\:\:{f}\left(\mathrm{2}\right)\:+\:{f}\left(\mathrm{3}\right)\:+\:{f}\left(\mathrm{4}\right)+\:…\:=? \\ $$ Commented by Frix last updated on 25/May/25…
Question Number 220869 by fantastic last updated on 20/May/25 $${Find}\:{the}\:{maximum}\:{value}\:{of}\:{x}^{\mathrm{2}} {y}^{\mathrm{3}} {z}^{\mathrm{4}} \:{subject}\:{to}\:{the}\:{condition}\:{x}+{y}+{z}=\mathrm{18} \\ $$ Commented by mr W last updated on 20/May/25 $${x},\:{y},\:{z}\:\in{N}\:\:\:{or}\:{Z}\:{or}\:{R}\:? \\…
Question Number 219733 by Spillover last updated on 01/May/25 Answered by SdC355 last updated on 01/May/25 $$\mid\mathrm{g}\left({x}\right)−\mathrm{2}\mid\leq\mathrm{3}\left({x}−\mathrm{1}\right)^{\mathrm{2}} \\ $$$$−\mathrm{3}\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{2}\leq\mathrm{g}\left({x}\right)\leq\mathrm{3}\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{2} \\ $$$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}−\mathrm{3}\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{2}\leq\underset{{x}\rightarrow\mathrm{1}}…
Question Number 219377 by golsendro last updated on 23/Apr/25 $$\:\mathrm{If}\:\left(\left(\mathrm{fog}\right)^{−\mathrm{1}} \mathrm{of}\right)\left(\mathrm{x}\right)=\:\mathrm{3x}−\mathrm{8} \\ $$$$\:\mathrm{find}\:\mathrm{g}\left(\mathrm{5}\right). \\ $$ Answered by Hanuda354 last updated on 23/Apr/25 $${g}^{−\mathrm{1}} \left({x}\right)\:=\:\mathrm{3}{x}−\mathrm{8} \\…