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Question Number 169182 by mathlove last updated on 25/Apr/22 $$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\frac{\pi{cos}\mathrm{2}{x}−{x}}{\mathrm{1}+{cosx}}=? \\ $$ Commented by infinityaction last updated on 25/Apr/22 $${use}\:{l}\:{hospital}\:{rule} \\ $$$$\:\:\:\:{p}\:\:\:=\:\:\:\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{−\mathrm{2}\pi\mathrm{sin}\:\mathrm{2}{x}\:−\:\mathrm{1}}{−\mathrm{sin}\:{x}} \\…
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Question Number 103603 by Quvonchbek last updated on 16/Jul/20 Commented by Quvonchbek last updated on 16/Jul/20 $${prove} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 169139 by Shrinava last updated on 24/Apr/22 Commented by Shrinava last updated on 26/Apr/22 $$\mathrm{Perfect}\:\mathrm{dear}\:\mathrm{sir}\:\mathrm{thankyou} \\ $$ Commented by mr W last updated…
Question Number 169130 by pete last updated on 24/Apr/22 $$\mathrm{If}\:\left(\mathrm{0}.\mathrm{3}\right)^{\mathrm{x}} =\left(\mathrm{0}.\mathrm{5}\right)^{\mathrm{8}} ,\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$ Answered by MikeH last updated on 24/Apr/22 $${x}\:=\:\frac{\mathrm{8}\:\mathrm{log}\:\mathrm{0}.\mathrm{5}}{\mathrm{log}\:\mathrm{0}.\mathrm{3}}\:=\mathrm{4}.\mathrm{6057} \\ $$ Commented…
Question Number 169120 by mnjuly1970 last updated on 24/Apr/22 $$ \\ $$$$\:\:\:\:{solve}\:\:{in}\:\mathbb{R} \\ $$$$\: \\ $$$$\:\:\:\:\:\lfloor\:\mathrm{log}_{\:\mathrm{2}} \left({x}\right)\:\rfloor=\:\mathrm{5}\:\mathrm{log}_{\:\mathrm{8}} \left(\sqrt{{x}}\:\right) \\ $$$$ \\ $$ Answered by aleks041103…
Question Number 169117 by infinityaction last updated on 24/Apr/22 Answered by greougoury555 last updated on 24/Apr/22 $$\:{f}\left({x},{y},\lambda\right)=\:\left({x}^{\mathrm{3}} +\mathrm{1}\right)\left({y}^{\mathrm{3}} +\mathrm{1}\right)+\lambda\left({x}+{y}−\mathrm{1}\right) \\ $$$$\:\frac{\partial{f}}{\partial{x}}\:=\:\mathrm{3}{x}^{\mathrm{2}} \left({y}^{\mathrm{3}} +\mathrm{1}\right)+\lambda=\mathrm{0} \\ $$$$\:\frac{\partial{f}}{\partial{y}}\:=\:\mathrm{3}{y}^{\mathrm{2}}…
Question Number 169092 by Shrinava last updated on 24/Apr/22 Answered by mr W last updated on 24/Apr/22 Commented by mr W last updated on 24/Apr/22…
Question Number 37991 by Fawomath last updated on 20/Jun/18 $$\mathrm{1}.\:{Find}\:{the}\:{sum} \\ $$$$\:\:\:\:{s}_{{n}} =\mathrm{1}+\mathrm{2}{x}+\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}^{\mathrm{3}} +…+{nx}^{{n}−\mathrm{1}} \\ $$$${Hence},{or}\:{otherwise},\:{find}\:{the}\:{sum} \\ $$$$\:\:\:\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}.\mathrm{2}^{{k}} \\ $$$$\mathrm{2}.\:{Simplify}\:{the}\:{following} \\ $$$${i}.\:\underset{{r}=\mathrm{0}}…