Menu Close

Category: None

If-log-x-3-y-3-x-3-y-3-then-dy-dx-

Question Number 160764 by ZiYangLee last updated on 06/Dec/21 $$\mathrm{If}\:\:\:\:\mathrm{log}\left(\frac{{x}^{\mathrm{3}} −{y}^{\mathrm{3}} }{{x}^{\mathrm{3}} +{y}^{\mathrm{3}} }\right),\:\mathrm{then}\:\frac{{dy}}{{dx}}=? \\ $$ Commented by cortano last updated on 06/Dec/21 $$\:\mathrm{do}\:\mathrm{you}\:\mathrm{meant}\:\mathrm{y}=\:\mathrm{ln}\:\left(\frac{\mathrm{x}^{\mathrm{3}} −\mathrm{y}^{\mathrm{3}}…

Question-160746

Question Number 160746 by Rokon last updated on 05/Dec/21 Answered by som(math1967) last updated on 06/Dec/21 $${if}\:\boldsymbol{\theta}=\mathrm{45}°\boldsymbol{{then}}\:\boldsymbol{{A}}=\sqrt{\mathrm{2}}\:\boldsymbol{{B}}=\mathrm{0} \\ $$$$\left.{ii}\right)\:{A}=\sqrt{\mathrm{2}}\left({cos}\theta+\boldsymbol{{sin}\theta}−{sin}\boldsymbol{\theta}\right) \\ $$$$\therefore\boldsymbol{{cos}\theta}+\boldsymbol{{sin}\theta}=\sqrt{\mathrm{2}}\boldsymbol{{cos}\theta} \\ $$$$\Rightarrow\boldsymbol{{sin}\theta}=\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)\boldsymbol{{cos}\theta} \\ $$$$\Rightarrow\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)\boldsymbol{{sin}\theta}=\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)\boldsymbol{{cos}\theta}…

Question-95202

Question Number 95202 by mathocean1 last updated on 23/May/20 Commented by PRITHWISH SEN 2 last updated on 24/May/20 $$\mathrm{x}=\mathrm{2}\left(\mathrm{2cos}^{\mathrm{2}} \theta−\mathrm{1}\right)−\mathrm{1}=\mathrm{2cos2}\theta−\mathrm{1} \\ $$$$\therefore\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{2}\right)^{\mathrm{2}} =\:\mathrm{4}…\left(\mathrm{i}\right) \\…

Question-95180

Question Number 95180 by mathocean1 last updated on 23/May/20 Commented by mathocean1 last updated on 23/May/20 $$\mathrm{Please}\:\mathrm{sirs}\:\mathrm{help}\:\mathrm{me}… \\ $$$$\mathrm{I}\:\mathrm{have}\:\mathrm{done}\:\mathrm{the}\:\mathrm{first}\:\mathrm{question}\:\mathrm{and}\:\mathrm{found} \\ $$$$\mathrm{as}\:\mathrm{result}\:\mathrm{25}. \\ $$ Terms of…

Prove-that-1-1-2-1-3-1-n-lt-2-n-

Question Number 160694 by naka3546 last updated on 04/Dec/21 $${Prove}\:\:{that}\:\: \\ $$$$\:\:\:\:\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\:+\:\ldots+\:\frac{\mathrm{1}}{\:\sqrt{{n}}}\:\:<\:\mathrm{2}\sqrt{{n}} \\ $$ Answered by mindispower last updated on 04/Dec/21 $$\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}}}=\frac{\mathrm{2}}{\mathrm{2}\sqrt{\mathrm{1}+{x}}}<\frac{\mathrm{2}}{\:\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}}=\mathrm{2}\left(\sqrt{\mathrm{1}+{x}}−\sqrt{{x}}\right) \\ $$$$\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}}…