Question Number 95325 by ~blr237~ last updated on 24/May/20 $$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\:\:\:\frac{\mathrm{1}}{{n}}{HCF}\left(\mathrm{20},{n}\right)\:=\:\mathrm{0}\:\:\:\:\:\:\:? \\ $$ Commented by mr W last updated on 24/May/20 $$\mathrm{1}\leqslant{HCF}\left(\mathrm{20},{n}\right)\leqslant\mathrm{20}\:{for}\:{n}\geqslant\mathrm{20} \\ $$$$\frac{\mathrm{1}}{{n}}\leqslant\frac{{HCF}\left(\mathrm{20},{n}\right)}{{n}}\leqslant\frac{\mathrm{20}}{{n}} \\…
Question Number 95323 by ~blr237~ last updated on 24/May/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\int_{{x}} ^{\mathrm{2}{x}} \:\frac{{ln}\left(\mathrm{2}+{t}\right)}{{t}}{dt}\:=\:\left({ln}\mathrm{2}\right)^{\mathrm{2}} \\ $$ Answered by abdomathmax last updated on 24/May/20 $$\left.\exists\:\mathrm{c}\in\right]\mathrm{x},\mathrm{2x}\left[\:/\:\int_{\mathrm{x}} ^{\mathrm{2x}} \:\frac{\mathrm{ln}\left(\mathrm{2}+\mathrm{t}\right)}{\mathrm{t}}\mathrm{dt}\:=\mathrm{ln}\left(\mathrm{2}+\mathrm{c}\right)\int_{\mathrm{x}}…
Question Number 29778 by puneet1789 last updated on 12/Feb/18 Answered by Giannibo last updated on 12/Feb/18 $$ \\ $$$$ \\ $$$$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}'\left(\mathrm{x}\right)\leqslant\mathrm{1} \\ $$$$\mathrm{e}^{\mathrm{x}} \mathrm{f}\left(\mathrm{x}\right)+\mathrm{e}^{\mathrm{x}} \mathrm{f}'\left(\mathrm{x}\right)\leqslant\mathrm{e}^{\mathrm{x}}…
Question Number 160837 by mnjuly1970 last updated on 07/Dec/21 Commented by cortano last updated on 07/Dec/21 $$\Leftrightarrow\:\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{4}} −\mathrm{2x}^{\mathrm{2}} +\mathrm{1}=\mathrm{x}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{1}\right) \\ $$$$\Leftrightarrow\mathrm{x}^{\mathrm{4}} −\mathrm{x}^{\mathrm{2}} +\mathrm{1}\:=\:\mathrm{x}^{\mathrm{3}}…
Question Number 29752 by Victor31926 last updated on 11/Feb/18 $$\mathrm{pls}\:\mathrm{elp}\:\mathrm{with}\:\mathrm{dis}… \\ $$$$ \\ $$$$\int\frac{\left(\mathrm{1}−\mathrm{x}\right)\boldsymbol{{dx}}}{\left(\mathrm{1}+\mathrm{x}\right)\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{3}} }} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 160822 by sdfg last updated on 07/Dec/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 160752 by Eric002 last updated on 05/Dec/21 $${solve} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−{y}={x}^{\mathrm{2}} {sin}\mathrm{3}{x} \\ $$ Answered by qaz last updated on 06/Dec/21 $$\mathrm{y}''−\mathrm{y}=\mathrm{x}^{\mathrm{2}}…
Question Number 29592 by zekeriyaozkan last updated on 10/Feb/18 $${y}'={xy}^{\mathrm{2}} +\mathrm{2}{y}+\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 160603 by cortano last updated on 03/Dec/21 $$\:\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\right)\left(\mathrm{y}+\sqrt{\mathrm{y}^{\mathrm{2}} +\mathrm{1}}\right)=\mathrm{2021} \\ $$$$\:\forall\mathrm{x},\mathrm{y}\in\mathbb{R}^{+} \:.\:\mathrm{min}\:\left(\mathrm{x}+\mathrm{y}\right)=? \\ $$ Answered by MJS_new last updated on 03/Dec/21 $$\mathrm{of}\:\mathrm{all}\:\mathrm{rectangles}\:\mathrm{with}\:\mathrm{sides}\:{a},\:{b}\:\mathrm{and}\:\mathrm{given}…
Question Number 160577 by mnjuly1970 last updated on 02/Dec/21 $$ \\ $$$$\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} {tan}^{\:−\mathrm{1}} \:\left({x}\right).{ln}\left({x}\right)\:=\:? \\ $$$$\:\:\:\:\:−−−−{solution}−−−− \\ $$$$\:\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\:\mathrm{1}} {tan}^{\:−\mathrm{1}} \left(\:{x}\right)\:.{x}^{\:{a}} {dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\:\underset{{n}=\mathrm{1}}…