Menu Close

Author: Tinku Tara

Question-127490

Question Number 127490 by ZiYangLee last updated on 30/Dec/20 Commented by mr W last updated on 30/Dec/20 $${Q}\mathrm{45}. \\ $$$$\frac{{dx}}{{dt}}=\mathrm{3}{t}^{\mathrm{2}} \\ $$$$\frac{{dy}}{{dt}}=\mathrm{2}{t} \\ $$$$\frac{{dy}}{{dx}}=\frac{\frac{{dy}}{{dt}}}{\frac{{dx}}{{dt}}}=\frac{\mathrm{2}{t}}{\mathrm{3}{t}^{\mathrm{2}} }=\frac{\mathrm{2}}{\mathrm{3}{t}}…

Question-193026

Question Number 193026 by Mingma last updated on 02/Jun/23 Answered by aleks041103 last updated on 02/Jun/23 $$\left(\mathrm{3}+\sqrt{\mathrm{5}}\right)^{\mathrm{3}} =\mathrm{3}^{\mathrm{3}} +\mathrm{3}×\mathrm{3}^{\mathrm{2}} ×\sqrt{\mathrm{5}}+\mathrm{3}×\mathrm{3}×\mathrm{5}+\mathrm{5}\sqrt{\mathrm{5}}= \\ $$$$=\mathrm{27}+\mathrm{45}+\mathrm{32}\sqrt{\mathrm{5}}=\mathrm{72}+\mathrm{32}\sqrt{\mathrm{5}} \\ $$$$\mathrm{32}\sqrt{\mathrm{5}}=\sqrt{\mathrm{5}×\mathrm{32}^{\mathrm{2}} }=\sqrt{\mathrm{5}×\mathrm{1024}}=\sqrt{\mathrm{5120}}=\mathrm{71}+{r}…

Question-127486

Question Number 127486 by shaker last updated on 30/Dec/20 Answered by Dwaipayan Shikari last updated on 30/Dec/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}{cos}\left({a}_{{k}} {x}\right)−\mathrm{1}}{{x}^{\mathrm{2}} }={y} \\ $$$$\underset{{x}\rightarrow\mathrm{0}}…