Question Number 200520 by malak last updated on 19/Nov/23 $$\:\:{x}/{x}+\mathrm{1}−{x}−\mathrm{1}/{x} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 200521 by brahim_mekkaoui last updated on 19/Nov/23 $$\mathrm{Let}\:{u}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{{n}}{{n}^{\mathrm{2}} +{k}^{\mathrm{2}} }\:\:\mathrm{for}\:{n}\in\mathbb{N}_{>\mathrm{0}} \:\:. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\left({u}_{{n}} \right)_{{n}>\mathrm{0}} \:\mathrm{is}\:\mathrm{increasing}. \\ $$ Terms of Service…
Question Number 200457 by cortano12 last updated on 19/Nov/23 Commented by cortano12 last updated on 19/Nov/23 $$\:\:\:\:\cancel{\boldsymbol{{x}}} \\ $$ Answered by mr W last updated…
Question Number 200459 by faysal last updated on 19/Nov/23 $$\mathrm{In}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{3}} −\mathrm{x}−\mathrm{1}=\mathrm{0},\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{s}_{\mathrm{6}} . \\ $$ Commented by Frix last updated on 19/Nov/23 $$\mathrm{What}\:\mathrm{is}\:“{s}_{\mathrm{6}} ''?…
Question Number 200519 by malak last updated on 19/Nov/23 $${x}/{x}+\mathrm{1}−{x}−\mathrm{1}/{x} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 200444 by Calculusboy last updated on 18/Nov/23 Answered by Frix last updated on 19/Nov/23 $$\int\mathrm{e}^{−\mathrm{i}{x}^{\mathrm{2}} } {dx}\:\overset{{t}=\mathrm{e}^{\mathrm{i}\frac{\pi}{\mathrm{4}}} {x}} {=} \\ $$$$=\frac{\sqrt{\mathrm{2}}\left(\mathrm{1}−\mathrm{i}\right)}{\mathrm{2}}\int\mathrm{e}^{−{t}^{\mathrm{2}} } {dt}=\frac{\sqrt{\mathrm{2}\pi}\left(\mathrm{1}−\mathrm{i}\right)}{\mathrm{4}}\int\frac{\mathrm{2e}^{{t}^{\mathrm{3}}…
Question Number 200446 by hardmath last updated on 18/Nov/23 $${fund}\:\:\:\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(\mathrm{3}\:+\:\left(−\mathrm{1}\right)^{\boldsymbol{{n}}} \right)^{\boldsymbol{{n}}} }{{n}}\:{x}^{\boldsymbol{{n}}} \:=\:? \\ $$ Answered by mr W last updated on 19/Nov/23…
Question Number 200377 by mr W last updated on 18/Nov/23 Commented by mr W last updated on 18/Nov/23 $${the}\:{side}\:{lengths}\:{of}\:{the}\:{hexagon}\:{are} \\ $$$${given}.\:{find}\:{x}+{y}+{z}=? \\ $$ Answered by…
Question Number 200379 by cortano12 last updated on 18/Nov/23 Commented by Frix last updated on 18/Nov/23 $$\mathrm{No}\:\mathrm{exact}\:\mathrm{solutions}\:\mathrm{possible}.\:\mathrm{Transform}\:\mathrm{to} \\ $$$$\begin{cases}{{y}^{\mathrm{2}} +\frac{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{\mathrm{2}\left({x}+\mathrm{1}\right)}{y}+\frac{{x}^{\mathrm{2}} +{x}−\mathrm{20}}{\mathrm{4}\left({x}+\mathrm{1}\right)}=\mathrm{0}}\\{{y}^{\mathrm{2}} +\frac{{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{6}}{\mathrm{2}{x}\left({x}+\mathrm{1}\right)}{y}+\frac{\mathrm{3}{x}−\mathrm{20}}{\mathrm{2}{x}\left({x}+\mathrm{1}\right)}=\mathrm{0}}\end{cases} \\…
Question Number 200438 by hardmath last updated on 18/Nov/23 $$\mathrm{Find}: \\ $$$$\sqrt{\mathrm{3}\:+\:\sqrt{\mathrm{6}\:+\:\sqrt{\mathrm{9}\:+\:…\:+\:\sqrt{\mathrm{96}\:+\:\sqrt{\mathrm{99}}}}}}\:=\:? \\ $$ Commented by Frix last updated on 19/Nov/23 $$\mathrm{There}'\mathrm{s}\:\mathrm{nothing}\:\mathrm{to}\:\mathrm{find},\:\mathrm{just}\:\mathrm{use}\:\mathrm{a}\:\mathrm{good} \\ $$$$\mathrm{calculator}. \\…