Question Number 1407 by 112358 last updated on 29/Jul/15 $${Solve}\:{the}\:{following}\:{inequality} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{sinx}+\mathrm{1}}{{cosx}}\leqslant\mathrm{1} \\ $$$${where}\:\mathrm{0}\leqslant{x}<\mathrm{2}\pi\:,\:{cosx}\neq\mathrm{0} \\ $$ Commented by 123456 last updated on 29/Jul/15 $${f}\left({x}\right)=\frac{\mathrm{sin}\:{x}+\mathrm{1}}{\mathrm{cos}\:{x}} \\…
Question Number 132478 by MathCoder last updated on 14/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 132473 by physicstutes last updated on 14/Feb/21 $$\int\:\frac{{x}\:\mathrm{cosh}\:{x}}{\left(\mathrm{sinh}\:{x}\right)^{\mathrm{2}} }\:{dx} \\ $$ Answered by mathmax by abdo last updated on 14/Feb/21 $$\mathrm{I}=\int\:\frac{\mathrm{xchx}}{\mathrm{sh}^{\mathrm{2}} \mathrm{x}}\mathrm{dx}\:\:\mathrm{by}\:\mathrm{parts}\:\:\mathrm{u}^{'} \:=\frac{\mathrm{chx}}{\mathrm{sh}^{\mathrm{2}}…
Question Number 66938 by Cmr 237 last updated on 20/Aug/19 Commented by mathmax by abdo last updated on 21/Aug/19 $$\left.\mathrm{8}\right){by}\:{parts}\:\:\int\:{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dx}\:={xln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)−\int\:{x}\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$={xln}\left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 132475 by Study last updated on 14/Feb/21 $${prove}\:{that}\:\:{x}_{\mathrm{1}} +{x}_{\mathrm{2}} =−\frac{{b}}{{a}} \\ $$$${x}_{\mathrm{1}} {and}\:{x}_{\mathrm{2}} {are}\:{roots}\:{of}\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$ Commented by MJS_new last updated on…
Question Number 132474 by bemath last updated on 14/Feb/21 $$\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{4sin}\:\left(\mathrm{x}\right)+\mathrm{1}}\:−\mathrm{cos}\:\left(\mathrm{x}\right) \\ $$$$\mathrm{is}\: \\ $$ Commented by EDWIN88 last updated on 14/Feb/21 Commented by…
Question Number 66937 by Cmr 237 last updated on 20/Aug/19 Answered by mr W last updated on 21/Aug/19 $${let}\:{t}=\mathrm{81}^{\mathrm{sin}^{\mathrm{2}} \:{x}} \\ $$$$\mathrm{81}^{\mathrm{cos}^{\mathrm{2}} \:{x}} =\mathrm{81}^{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \:{x}}…
Question Number 132469 by Algoritm last updated on 14/Feb/21 Answered by Olaf last updated on 15/Feb/21 $$\mathrm{Let}\:\Omega_{{i}} \:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}_{{i}} \left(\mathrm{1}−\mathrm{ln}{x}_{{i}} \right)}{dx}_{{i}} \\ $$$$\mathrm{Let}\:{u}_{{i}} \:=\:\mathrm{1}−\mathrm{ln}{x}_{{i}}…
Question Number 66932 by Tinkutara@ last updated on 20/Aug/19 $${which}\:{of}\:{the}\:{sequences}\:{converges}\:? \\ $$$$\left.\mathrm{1}\right)\:{a}_{{n}} =\:{n}−\frac{\mathrm{1}}{{n}} \\ $$$$\left.\mathrm{2}\right)\:{a}_{{n}} =\:\left(\left(−\mathrm{1}\right)^{{n}} +\mathrm{1}\right)\left(\frac{{n}+\mathrm{1}}{{n}}\right) \\ $$ Answered by turbo msup by abdo…
Question Number 1397 by 314159 last updated on 28/Jul/15 $${Arrange}\:\mathrm{8}\:{coins}\:{in}\:{one}\:{line}\:{on}\:{a}\:{table} \\ $$$${such}\:{that}\:{the}\:{head}\:{or}\:{tail}\:{will}\:{be}\:{facing} \\ $$$${upward}.{Try}\:{to}\:{flip}\:{two}\:{neighboring}\:{coins}\: \\ $$$${that}\:{are}\:{not}\:{with}\:{identical}\:{face}\:{upside}\:{down}.{After}\: \\ $$$${several}\:{operations}\:,\:{how}\:{many}\:{different}\: \\ $$$${ways}\:{can}\:{the}\:{heads}\:{and}\:{tails}\:{be}\:{arranged} \\ $$$${in}\:{one}\:{line}\:{on}\:{the}\:{table}. \\ $$ Commented…