Question Number 212140 by mnjuly1970 last updated on 03/Oct/24 $$ \\ $$$$\:\mathrm{I}{f},\:\:\:\:\:{f}\left({x}\right)=−\:{x}^{\mathrm{2}} \:+\mathrm{4}{x}\:−\mathrm{3}\: \\ $$$$\:\:\:\:\: \\ $$$$,\:{g}\left({x}\right)=\:\begin{cases}{\:\sqrt{\mathrm{7}−{x}}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\:<\mathrm{7}}\\{\:\:\lfloor\:\mathrm{5}{x}\:\rfloor\:−\mathrm{5}{x}\:\:\:\:\:\:\:\:{x}\geqslant\mathrm{7}}\end{cases}\:\:\: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\:\:\:{R}_{{fog}} \:=\:\left({a}\:,{b}\right]\:\: \\ $$$$\:\:\:\:\:\:\:{find}\:\:{the}\:{value}\:{of}\:\:\:{b}−{a} \\…
Question Number 212136 by Subhi last updated on 03/Oct/24 $${what}\:{is}\:{the}\:{maximal}\:{number}\:{of}\:{consecutive}\:{natural} \\ $$$${numbers}\:{which}\:{are}\:{coprime}\:{with}\:{the} \\ $$$${sum}\:{of}\:{their}\:{divisors} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212123 by MrGaster last updated on 02/Oct/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{solve}\:\mathrm{an}\:\mathrm{equation}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\boldsymbol{\mathrm{ln}}\:\boldsymbol{{x}}}=\boldsymbol{\mathrm{ln}}\sqrt{\boldsymbol{{x}}} \\ $$ Answered by Frix last updated on 02/Oct/24 $$\sqrt{\mathrm{ln}\:{x}}=\frac{\mathrm{ln}\:{x}}{\mathrm{2}} \\…
Question Number 212098 by CrispyXYZ last updated on 30/Sep/24 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{ln}\:\frac{\sqrt{\mathrm{13}}−\mathrm{1}}{\mathrm{10}}\:+\:\sqrt{\mathrm{13}}\:−\:\mathrm{2}\:>\mathrm{0} \\ $$$$\mathrm{without}\:\mathrm{calculator}. \\ $$ Answered by MrGaster last updated on 03/Nov/24 $$\mathrm{ln}\left(\sqrt{\mathrm{13}}−\mathrm{1}\right)−\mathrm{ln}\:\mathrm{10}+\sqrt{\mathrm{13}}−\mathrm{2}>\mathrm{0} \\…
Question Number 212094 by behi834171 last updated on 29/Sep/24 $$\left[\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{4}}}+…….+\frac{\mathrm{1}}{\:\sqrt{\mathrm{1000000}}}\right]=? \\ $$$$\boldsymbol{{note}}:\:\:\:\left[\mathrm{6}.\mathrm{25}\right]=\mathrm{6}\:\:\:,\left[\mathrm{0}.\mathrm{47}\right]=\mathrm{0} \\ $$ Answered by fabricio2008 last updated on 30/Sep/24 $$\underset{{x}=\mathrm{1}} {\overset{\mathrm{10}^{\mathrm{6}} } {\sum}}\left(\sqrt{{x}}\right)^{-\mathrm{1}}…
Question Number 212084 by Spillover last updated on 28/Sep/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212052 by Spillover last updated on 28/Sep/24 Answered by Ghisom last updated on 28/Sep/24 $$\int\frac{{dx}}{\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} }= \\ $$$$\:\:\:\:\:\left[\mathrm{Ostrogradski}'\mathrm{s}\:\mathrm{M}\:\mathrm{ethod}\right] \\ $$$$=−\frac{{x}}{\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{1}}= \\…
Question Number 212049 by Spillover last updated on 28/Sep/24 Answered by Ghisom last updated on 28/Sep/24 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{{dx}}{\:\sqrt{−\mathrm{ln}\:{x}}}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{−\mathrm{ln}\:{x}}\right] \\ $$$$=−\mathrm{2}\underset{\infty} {\overset{\mathrm{0}} {\int}}\mathrm{e}^{−{t}^{\mathrm{2}}…
Question Number 212048 by Spillover last updated on 28/Sep/24 Answered by Ghisom last updated on 28/Sep/24 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{dx}}{\:\sqrt{{x}}\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\sqrt{{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}}= \\ $$$$\:\:\:\:\:\left[{t}={x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right] \\…
Question Number 212085 by hardmath last updated on 28/Sep/24 $$\mathrm{a},\mathrm{b},\mathrm{c}\:\in\:\mathbb{N} \\ $$$$\mathrm{5a}\:+\:\mathrm{6b}\:+\:\mathrm{7c}\:=\:\mathrm{70} \\ $$$$\mathrm{find}:\:\:\mathrm{max}\left(\mathrm{a}\right)\:=\:? \\ $$ Commented by Frix last updated on 28/Sep/24 $$\mathrm{If}\:\mathrm{0}\in\mathbb{N}\:\Rightarrow\:\mathrm{max}\:{a}\:=\mathrm{14}\:\:\:\:\:\left({b}={c}=\mathrm{0}\right) \\…