Question Number 148482 by mathdanisur last updated on 28/Jul/21 Commented by hknkrc46 last updated on 28/Jul/21 $$\bigstar\:\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{2}}{\mathrm{79}}\:+\:\frac{\mathrm{3}}{\mathrm{80}}\:−\:\mathrm{3} \\ $$$$=\:\left(\frac{\mathrm{1}}{\mathrm{78}}\:−\:\mathrm{1}\right)\:+\:\left(\frac{\mathrm{2}}{\mathrm{79}}\:−\:\mathrm{1}\right)\:+\:\left(\frac{\mathrm{3}}{\mathrm{80}}\:−\:\mathrm{1}\right) \\ $$$$=\:\frac{−\mathrm{77}}{\mathrm{78}}\:+\:\frac{−\mathrm{77}}{\mathrm{79}}\:+\:\frac{−\mathrm{77}}{\mathrm{80}} \\ $$$$=\:−\mathrm{77}\left(\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{1}}{\mathrm{79}}\:+\:\frac{\mathrm{1}}{\mathrm{80}}\right) \\ $$$$\bigstar\:\frac{−\mathrm{77}\left(\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{1}}{\mathrm{79}}\:+\:\frac{\mathrm{1}}{\mathrm{80}}\right)}{\frac{\mathrm{1}}{\mathrm{78}}\:+\:\frac{\mathrm{1}}{\mathrm{79}}\:+\:\frac{\mathrm{1}}{\mathrm{80}}}\:=\:−\mathrm{77}…
Question Number 148453 by mathdanisur last updated on 28/Jul/21 $$\frac{\left({n}\:+\:\mathrm{1}\right)!}{{n}!}\:=\:\mathrm{38}\:\:\Rightarrow\:\:{n}=? \\ $$ Answered by puissant last updated on 28/Jul/21 $$\Rightarrow\frac{\left(\mathrm{n}+\mathrm{1}\right)×\mathrm{n}!}{\mathrm{n}!}=\mathrm{38} \\ $$$$\Rightarrow\mathrm{n}+\mathrm{1}=\mathrm{38} \\ $$$$\Rightarrow\mathrm{n}=\mathrm{37}.. \\…
Question Number 148452 by mathdanisur last updated on 28/Jul/21 $$\underset{\:\mathrm{1}} {\overset{\:\mathrm{4}} {\int}}\mathrm{2}{sin}^{\mathrm{2}} {x}\:{dx}\:+\:\underset{\:\mathrm{1}} {\overset{\:\mathrm{4}} {\int}}\left(\mathrm{1}+{cos}\mathrm{2}{x}\right){dx}\:=\:? \\ $$ Answered by puissant last updated on 28/Jul/21 $$=\int_{\mathrm{1}}…
Question Number 148454 by mathdanisur last updated on 28/Jul/21 $${sin}^{\mathrm{6}} \boldsymbol{\alpha}\:+\:{co}^{\mathrm{6}} \boldsymbol{\alpha}\:=\:\frac{\mathrm{3}}{\mathrm{4}}\:\:\Rightarrow\:\:\mathrm{6}{cos}\mathrm{4}\boldsymbol{\alpha}=? \\ $$$$ \\ $$ Answered by Ar Brandon last updated on 28/Jul/21 $$\mathrm{sin}^{\mathrm{6}}…
Question Number 148445 by mathdanisur last updated on 28/Jul/21 $${if}\:\:\:{cos}\boldsymbol{\alpha}\:=\:\sqrt{\boldsymbol{{a}}} \\ $$$${find}\:\:\:\mathrm{5}\:-\:\mathrm{6}{cos}\mathrm{2}\boldsymbol{\alpha}\:+\:{cos}\mathrm{4}\boldsymbol{\alpha}\:=\:? \\ $$ Commented by mathdanisur last updated on 28/Jul/21 $${Thank}\:{you}\:{Ser} \\ $$$${But},\:=\sqrt{\boldsymbol{\alpha}}\:\left({alfa}\:{no}\right)\:\:=\sqrt{\boldsymbol{{a}}} \\…
Question Number 82897 by aseer imad last updated on 25/Feb/20 Commented by mr W last updated on 25/Feb/20 $${certainly}! \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{f}\left({x}\right)={f}\left(\mathrm{0}\right)=\mathrm{0}+\mathrm{1}+\mathrm{2}=\mathrm{3} \\ $$$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{f}\left({x}\right)={f}\left(\mathrm{1}\right)=\mathrm{1}+\mathrm{0}+\mathrm{1}=\mathrm{2}…
Question Number 148421 by mathdanisur last updated on 27/Jul/21 $$\underset{\boldsymbol{{x}}\rightarrow\infty} {{lim}}\frac{{cos}\left({x}\right)\:-\:{x}!}{\mathrm{3}^{\boldsymbol{{x}}} \:-\:\mathrm{4}^{\boldsymbol{{x}}} }\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 148416 by mathdanisur last updated on 27/Jul/21 $$\underset{\boldsymbol{{x}}\rightarrow\infty} {{lim}}\frac{{x}!\:-\:{cos}\left(\mathrm{2}{x}\right)}{\mathrm{3}{x}\:+\:\mathrm{1}}\:=\:? \\ $$ Answered by mathmax by abdo last updated on 28/Jul/21 $$\mathrm{we}\:\mathrm{have}\:\frac{\mathrm{x}!−\mathrm{cos}\left(\mathrm{2x}\right)}{\mathrm{3x}+\mathrm{1}}=\frac{\mathrm{x}!}{\mathrm{3x}+\mathrm{1}}−\frac{\mathrm{cos}\left(\mathrm{2x}\right)}{\mathrm{3x}+\mathrm{1}} \\ $$$$\mathrm{lim}_{\mathrm{x}\rightarrow+\infty}…
Question Number 148418 by mathdanisur last updated on 27/Jul/21 $${Find}\:{the}\:{natural}\:{roots}\:{of}\:{the}\:{equation} \\ $$$${x}^{\mathrm{2}} \:-\:\mathrm{51}{y}^{\mathrm{2}} \:=\:\mathrm{1} \\ $$ Answered by mr W last updated on 27/Jul/21 $${x}^{\mathrm{2}}…
Question Number 82881 by jagoll last updated on 25/Feb/20 $$ \\ $$$$\sqrt{\sqrt{…\sqrt{\mathrm{6561}}}}\:=\:\mathrm{3}^{\mathrm{8}^{\mathrm{x}} } \:\left(\mathrm{60}\:\mathrm{times}\right) \\ $$$$\mathrm{find}\:\mathrm{x} \\ $$ Commented by mr W last updated on…