Question Number 221369 by mr W last updated on 01/Jun/25 Commented by mr W last updated on 01/Jun/25 $${no} \\ $$ Commented by fantastic last…
Question Number 221370 by mr W last updated on 01/Jun/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221367 by SdC355 last updated on 01/Jun/25 $$\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \:\:\frac{\mathrm{1}}{\mathrm{5}−\mathrm{4sin}\left(\theta\right)}\:\mathrm{d}\theta=?? \\ $$$$\left(\mathrm{Complex}\:\mathrm{integral}\:\mathrm{method}\right) \\ $$ Answered by vnm last updated on 03/Jun/25 $$\int_{\mathrm{0}} ^{\mathrm{2}\pi}…
Question Number 221377 by hardmath last updated on 01/Jun/25 $$\mathrm{Find}:\:\:\:\Omega\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{2}\:\sqrt[{\boldsymbol{\mathrm{n}}}]{\mathrm{10}}\:−\:\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} \:=\:? \\ $$ Answered by Ghisom last updated on 01/Jun/25 $$\mathrm{ln}\:\Omega\:=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}\mathrm{ln}\:\left(\mathrm{2}×\mathrm{10}^{\mathrm{1}/{n}} −\mathrm{1}\right) \\…
Question Number 221342 by universe last updated on 31/May/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221360 by Nicholas666 last updated on 31/May/25 $$ \\ $$$$\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \:\mathrm{cos}^{−\mathrm{1}} \:\left(\frac{\mathrm{cos}\:{x}}{\mathrm{1}\:+\:\mathrm{2}\:\mathrm{cos}\:{x}}\right)\:\mathrm{d}{x} \\ $$$$ \\ $$ Answered by MrGaster last updated on…
Question Number 221359 by Engr_Jidda last updated on 31/May/25 Answered by Rasheed.Sindhi last updated on 31/May/25 $${x}\ast{y}=\mathrm{2}{x}+\mathrm{2}{y}−\frac{{xy}}{\mathrm{5}} \\ $$$${let}\:{e}\:{is}\:{an}\:{identity}\:{element}\:{of}\:\ast \\ $$$${x}\ast{e}={e}\ast{x}={x} \\ $$$$\Rightarrow\mathrm{2}{x}+\mathrm{2}{e}−\frac{{xe}}{\mathrm{5}}={x} \\ $$$${e}\left(\frac{\mathrm{10}−{x}}{\mathrm{5}}\right)=−{x}…
Question Number 221352 by Nicholas666 last updated on 31/May/25 $$ \\ $$$$\:\:\:\:\mathrm{Given}\:\mathrm{real}\:\mathrm{numbers}\:{a},{b},{c}\:>\:\mathrm{0}\:, \\ $$$$\:\:\mathrm{such}\:\mathrm{that}\:{a}\:+\:{b}\:+\:{c}\:=\:{a}^{\mathrm{3}} \:+\:{b}^{\mathrm{3}} \:+\:{c}^{\mathrm{3}} \:, \\ $$$$\:\mathrm{Prove}\:;\:\frac{{a}^{\mathrm{3}} }{{a}^{\mathrm{4}} \:+\:{b}\:+\:{c}}\:+\:\frac{{b}^{\mathrm{3}} }{{b}^{\mathrm{4}} \:+\:{c}\:+\:{a}}\:+\:\frac{{c}^{\mathrm{3}} }{{c}^{\mathrm{4}} \:+\:\:{a}\:+\:{b}}\:\leqslant\:\mathrm{1}…
Question Number 221354 by Nicholas666 last updated on 31/May/25 $$ \\ $$$$\:\:\mathrm{Let}\:{a},{b},{c}\:\mathrm{be}\:\mathrm{there}\:\mathrm{real}\:\mathrm{numbers}, \\ $$$$\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}; \\ $$$$\:\mathrm{sin}\:{a}\:+\:\mathrm{sin}\:{b}\:+\:\mathrm{sin}\:{c}\:\geqslant\:\mathrm{2}\:\:\Rightarrow\:\mathrm{cos}\:{a}\:+\:\mathrm{cos}\:{b}\:+\:\mathrm{cos}\:{c}\:\leqslant\:\sqrt{\mathrm{5}}\:\:\:\:\:\:\:\:\:\: \\ $$$$\mathrm{and}, \\ $$$$\:\mathrm{sin}\:{a}\:+\:\mathrm{sin}\:{b}\:+\:\mathrm{sin}\:{c}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{2}}\:\Rightarrow\:\mathrm{cos}\left({a}−\pi/\mathrm{6}\right)\:+\:\mathrm{cos}\left({b}−\pi/\mathrm{6}\right)\:+\:\mathrm{cos}\left({c}−\pi/\mathrm{6}\right)\:\geqslant\:\mathrm{0}\:.\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Commented…
Question Number 221348 by RoseAli last updated on 31/May/25 $$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{4}−\mathrm{2}^{{x}} }{{x}−\mathrm{2}} \\ $$ Answered by mr W last updated on 31/May/25 $$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{4}\left(\mathrm{1}−\mathrm{2}^{{x}} \right)}{{x}}…