Question Number 15234 by mrW1 last updated on 08/Jun/17 $$\mathrm{A}\:\mathrm{question}\:\mathrm{related}\:\mathrm{to}\:\mathrm{Q}.\mathrm{15184} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{ln}\:\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \\ $$ Commented by mrW1 last updated on 09/Jun/17 $$\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{ln}\:\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \:\mathrm{is}\:\left[\mathrm{1},+\infty\right) \\ $$$$\mathrm{let}\:\mathrm{t}=\frac{\mathrm{1}}{\mathrm{x}},\:\mathrm{t}\in\left(\mathrm{0},\mathrm{1}\right]…
Question Number 80760 by Power last updated on 06/Feb/20 Commented by mr W last updated on 06/Feb/20 $${f}\left({x}\right)={x} \\ $$ Terms of Service Privacy Policy…
Question Number 146285 by mathdanisur last updated on 12/Jul/21 $$\int\:{sin}\left(\mathrm{2}{x}\:-\:\frac{\pi}{\mathrm{4}}\right)\:{dx}\:=\:? \\ $$ Commented by gsk2684 last updated on 12/Jul/21 $${what}\:{are}\:{you}\:{studying}\:{now}? \\ $$ Commented by mathdanisur…
Question Number 146277 by mathdanisur last updated on 12/Jul/21 $$\int{cos}\left(\mathrm{2}{x}\right){dx}=? \\ $$ Answered by physicstutes last updated on 12/Jul/21 $$\mathrm{Nice}\:\mathrm{question}.\:\mathrm{lol} \\ $$$$\int\mathrm{cos}\:\left(\mathrm{2}{x}\right)\:{dx}\:=\:\frac{\mathrm{sin}\:\mathrm{2}{x}}{\mathrm{2}}+{k} \\ $$$$\int\mathrm{cos}\:\left({ax}\right){dx}\:=\:\frac{\mathrm{sin}\:{ax}}{{a}}+{k} \\…
Question Number 80747 by Power last updated on 06/Feb/20 Commented by MJS last updated on 06/Feb/20 $$\mathrm{we}\:\mathrm{had}\:\mathrm{this}\:\mathrm{weeks}\:\mathrm{ago}.\:\mathrm{it}'\mathrm{s}\:\mathrm{getting}\:\mathrm{boring}… \\ $$ Answered by tw000001 last updated on…
Question Number 146272 by mathdanisur last updated on 12/Jul/21 $${log}_{\boldsymbol{{x}}} \left({x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\:\leqslant\:\mathrm{1} \\ $$ Commented by iloveisrael last updated on 13/Jul/21 $$\:\mathrm{log}\:_{\mathrm{x}} \left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\leqslant\mathrm{log}\:_{\mathrm{x}} \left(\mathrm{x}\right)…
Question Number 80733 by key of knowledge last updated on 05/Feb/20 $$\mathrm{x}^{\mathrm{2}} =\mathrm{2}^{\mathrm{x}} \Rightarrow\mathrm{x}=? \\ $$ Commented by mr W last updated on 05/Feb/20 $${x}^{\mathrm{2}}…
Question Number 146261 by mathdanisur last updated on 12/Jul/21 $$\mathrm{4}\:{cos}\:\left(\mathrm{50}°\right)\:-\:\frac{\mathrm{1}}{{sin}\:\left(\mathrm{20}°\right)}\:=\:? \\ $$ Answered by bemath last updated on 12/Jul/21 $$\:\frac{\mathrm{4cos}\:\mathrm{50}°.\mathrm{cos}\:\mathrm{70}°−\mathrm{1}}{\mathrm{sin}\:\mathrm{20}°}\:= \\ $$$$\:\frac{\mathrm{2}\left(\mathrm{cos}\:\mathrm{120}°+\mathrm{cos}\:\mathrm{20}°\right)−\mathrm{1}}{\mathrm{sin}\:\mathrm{20}°}\:= \\ $$$$\:\frac{−\mathrm{1}+\mathrm{2cos}\:\mathrm{20}°−\mathrm{1}}{\mathrm{sin}\:\mathrm{20}°}\:=\: \\…
Question Number 146253 by mathdanisur last updated on 12/Jul/21 $$\left(\mathrm{4}{x}^{\mathrm{4}} \:-\:\mathrm{2}{x}^{\mathrm{2}} \:+\:\mathrm{17}\right)_{\boldsymbol{{max}}} \:=\:? \\ $$ Answered by iloveisrael last updated on 12/Jul/21 $$\mathrm{f}\left(\mathrm{x}\right)_{\mathrm{min}} =\:\mathrm{4}\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{2}} −\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{4}}\right)+\mathrm{17}…
Question Number 146244 by mathdanisur last updated on 12/Jul/21 $$\left(\sqrt{\mathrm{5}}\:-\:\mathrm{2}\right)^{\frac{\mathrm{2}{x}^{\mathrm{2}} -\mathrm{1}}{\mathrm{2}}} \:\:=\:\left(\sqrt{\mathrm{5}}\:+\:\mathrm{2}\right)^{\frac{\mathrm{3}{x}-\mathrm{7}}{\mathrm{4}}} \:\:\Rightarrow\:\:{x}=? \\ $$ Answered by gsk2684 last updated on 12/Jul/21 $${use}\:\sqrt{\mathrm{5}}−\mathrm{2}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}+\mathrm{2}} \\ $$$${compare}\:{exponents}…