Question Number 215979 by alcohol last updated on 23/Jan/25 $${u}_{{n}} \:=\:\underset{{k}={n}+\mathrm{1}} {\overset{\mathrm{2}{n}} {\sum}}\frac{\mathrm{1}}{{k}}\:{and}\:{v}_{{n}} \:=\:\underset{{k}={n}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}\frac{\mathrm{1}}{{k}} \\ $$$$\bullet\:{show}\:{that}\:{u}_{{n}} \:{and}\:{v}_{{n}} \:{are}\:{adjacent} \\ $$$${use}\:{ln}\left({x}+\mathrm{1}\right)\:\leqslant\:{x}\:{and}\:{x}\leqslant−{ln}\left(\mathrm{1}−{x}\right)\:{and} \\ $$$$\bullet\:{show}\:{that}\:{u}_{{n}} \:\leqslant\:\underset{{k}={n}+\mathrm{1}}…
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Question Number 215958 by Tawa11 last updated on 22/Jan/25 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{only}\:\mathrm{function}\:\mathrm{that}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{expression}\:\mathrm{below}: \\ $$$$\:\:\:\:\:\:\:\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{\mathrm{2}} \:\:=\:\:\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} } \\ $$ Answered by Ghisom last updated on…
Question Number 215809 by efronzo1 last updated on 18/Jan/25 $$\:\:\:\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{2}\:+\:\underset{\mathrm{1}} {\overset{−\mathrm{x}^{\mathrm{3}} } {\int}}\sqrt{\mathrm{2}+\mathrm{u}^{\mathrm{2}} }\:\mathrm{du}\: \\ $$$$\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{d}}{\mathrm{dx}}\:\left[\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)\right]_{\mathrm{x}=\mathrm{2}} \\ $$ Answered by mr W last updated…
Question Number 215528 by alephnull last updated on 09/Jan/25 Commented by mr W last updated on 10/Jan/25 $${this}\:{is}\:{not}\:{a}\:{question},\:{actually}\:{pure} \\ $$$${non}−{sense}\:{with}\:{a}\:{lot}\:{of} \\ $$$${mathematical}\:{symbols}\:{stacked} \\ $$$${together}. \\…
Question Number 215199 by efronzo1 last updated on 31/Dec/24 $$\:\:\:\:\:\downharpoonleft\underline{\:} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 214726 by universe last updated on 18/Dec/24 $$\mathrm{for}\:\mathrm{the}\:\mathrm{function}\:{z}\:=\:{x}\mathrm{tan}^{−\mathrm{1}} \left(\frac{{y}}{{x}}\right)+{y}\mathrm{sin}^{−\mathrm{1}} \left(\frac{{x}}{{y}}\right)+\mathrm{2} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\frac{\partial{z}}{\partial{x}}+{y}\frac{\partial{z}}{\partial{y}}=?\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 214335 by depressiveshrek last updated on 05/Dec/24 $$\mathrm{For}\:\mathrm{what}\:\mathrm{values}\:\mathrm{of}\:{k}\:\mathrm{does}\:\mathrm{the}\:\mathrm{equation} \\ $$$${e}^{{kx}} =\mathrm{3}\sqrt{{x}}\:\mathrm{have}\:\mathrm{only}\:\mathrm{one}\:\mathrm{solution}\:\mathrm{in}\:\mathbb{R}? \\ $$ Answered by mr W last updated on 06/Dec/24 $${y}={e}^{{kx}} \:{and}\:{y}=\mathrm{3}\sqrt{{x}}\:{should}\:{have}\:{only}…
Question Number 214000 by golsendro last updated on 24/Nov/24 $$\:\:\mathrm{Let}\:\mathrm{y}\left(\mathrm{x}\right)\:\mathrm{be}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{diff}\:\mathrm{eq}. \\ $$$$\:\:\mathrm{y}\:'=\:\frac{\mathrm{cos}\:\mathrm{x}+\mathrm{y}}{\mathrm{cos}\:\mathrm{x}}\:,\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\:\:\mathrm{Find}\:\mathrm{y}\left(\frac{\pi}{\mathrm{6}}\right). \\ $$ Commented by mr W last updated on 24/Nov/24 $${do}\:{you}\:{mean}\:\mathrm{cos}\:\left({x}+{y}\right)\:{instead}\:{of}…
Question Number 213664 by 281981 last updated on 13/Nov/24 Answered by mr W last updated on 13/Nov/24 Commented by mr W last updated on 13/Nov/24…