Question Number 166435 by mnjuly1970 last updated on 20/Feb/22 $$ \\ $$$$\:\:\:\:\mathscr{E}{quation}\:: \\ $$$$\:\:\:\:\:{Solve}\:{in}\:\:\mathbb{R}\: \\ $$$$\:\:\:\lfloor{x}\rfloor\:+\lfloor\mathrm{2}{x}\:\rfloor\:+\lfloor\:\mathrm{3}{x}\:\rfloor=\mathrm{1} \\ $$$$\:\:\:\:\:\:−−−−−−−−− \\ $$ Answered by mahdipoor last updated…
Question Number 166331 by mr W last updated on 18/Feb/22 $${prove}\:{that} \\ $$$$\frac{{df}^{−\mathrm{1}} \left({a}\right)}{{dx}}×\frac{{df}\left({f}^{−\mathrm{1}} \left({a}\right)\right)}{{dx}}=\mathrm{1} \\ $$ Commented by mr W last updated on 19/Feb/22…
Question Number 35248 by Raj Singh last updated on 17/May/18 Commented by Joel579 last updated on 17/May/18 $$\mathrm{Would}\:\mathrm{u}\:\mathrm{like}\:\mathrm{to}\:\mathrm{translate}\:\mathrm{into}\:\mathrm{English}? \\ $$ Terms of Service Privacy Policy…
Question Number 166294 by cortano1 last updated on 18/Feb/22 $$\:\mathrm{f}\left(\mathrm{x}\right)=\int_{\mathrm{1}} ^{{x}} \:\frac{{dt}}{\:\sqrt{{t}^{\mathrm{3}} +\mathrm{2}{t}^{\mathrm{2}} +\mathrm{3}}} \\ $$$$\:\:\:\left({f}^{−\mathrm{1}} \left(\mathrm{0}\right)\right)'=? \\ $$ Commented by cortano1 last updated on…
Question Number 166257 by mnjuly1970 last updated on 16/Feb/22 $$ \\ $$$$\:\:\:\lfloor{x}\rfloor\lfloor\mathrm{2}{x}\rfloor\lfloor\mathrm{3}{x}\rfloor=\:\mathrm{6} \\ $$$$\:\:\:\:\:\:\:{x}=\overset{} {?}\: \\ $$ Commented by MJS_new last updated on 16/Feb/22 $$\mathrm{1}\leqslant{x}<\frac{\mathrm{4}}{\mathrm{3}}…
Question Number 166254 by mnjuly1970 last updated on 16/Feb/22 $$ \\ $$$$\:\:\:\:\Theta=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:{H}_{\:{n}} }{{n}.\:\left({n}+\mathrm{1}\:\right)}\:\:\overset{?} {=}\:\frac{\pi^{\:\mathrm{2}} }{\mathrm{6}} \\ $$$$\:\:\:\:\:−−−−+ \\ $$ Answered by Kamel_Ben last…
Question Number 166246 by mnjuly1970 last updated on 16/Feb/22 Answered by Mathspace last updated on 18/Feb/22 $${I}=_{{by}\:{parts}} \:\:\left[\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right){ln}^{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)\right]_{\mathrm{0}} ^{\mathrm{1}} \\ $$$$−\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right).\mathrm{2}{ln}\left(\mathrm{1}−{x}^{\mathrm{2}}…
Question Number 35084 by Raj Singh last updated on 15/May/18 Commented by tanmay.chaudhury50@gmail.com last updated on 15/May/18 Answered by tanmay.chaudhury50@gmail.com last updated on 15/May/18 $${y}={tan}^{−\mathrm{1}}…
Question Number 166082 by mnjuly1970 last updated on 12/Feb/22 $$ \\ $$$$\:\:\:\:\:\:\:{prove} \\ $$$$\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\left(\mathrm{1}−{x}\:\right)^{\:\mathrm{2}} .{ln}^{\:\mathrm{3}} \left(\mathrm{1}−{x}\:\right)}{{x}}\:{dx}\:=\:\frac{\mathrm{51}}{\mathrm{8}}\:−\frac{\pi^{\:\mathrm{4}} }{\mathrm{15}}\:\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n} \\ $$$$\:\:\:\:\:\:\: \\ $$$$ \\ $$…
Question Number 34912 by abdo imad last updated on 12/May/18 $${let}\:{f}\left({x},{y},{z}\right)\:=\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)^{\alpha} \:\:\:\:\:{with}\:\alpha\in{R} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\Delta{f} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\alpha\:{in}\:{order}\:{to}\:{have}\:\Delta{f}=\mathrm{0} \\ $$ Answered by tanmay.chaudhury50@gmail.com last…