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Category: Differentiation

Let-n-1-and-integer-P-n-X-1-X-n-1-X-n-1-Factorize-P-n-2-Deduce-S-n-k-1-n-4-cotan-2-kpi-2n-1-

Question Number 125760 by snipers237 last updated on 13/Dec/20 $${Let}\:{n}\geqslant\mathrm{1}\:{and}\:{integer},\:{P}_{{n}} \left({X}\right)=\left(\mathrm{1}+{X}\right)^{{n}} −\left(\mathrm{1}−{X}\right)^{{n}} \: \\ $$$$\left.\mathrm{1}\right)\:{Factorize}\:{P}_{{n}} \\ $$$$\left.\mathrm{2}\right){Deduce}\:\:{S}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left[\mathrm{4}+{cotan}^{\mathrm{2}} \left(\frac{{k}\pi}{\mathrm{2}{n}+\mathrm{1}}\right)\:\right] \\ $$ Answered by…

P-o-1-P-1-1-X-and-for-all-n-1-P-n-1-P-n-XP-n-1-Explicit-P-n-and-prove-that-its-roots-are-all-real-

Question Number 125736 by snipers237 last updated on 13/Dec/20 $${P}_{{o}} =\mathrm{1}\:\:,{P}_{\mathrm{1}} =\mathrm{1}+{X}\:{and}\:{for}\:{all}\:{n}\geqslant\mathrm{1} \\ $$$${P}_{{n}+\mathrm{1}} ={P}_{{n}} +{XP}_{{n}−\mathrm{1}} \: \\ $$$${Explicit}\:\:{P}_{{n}} \:\:{and}\:{prove}\:{that}\:{its}\:{roots}\:{are}\:{all}\:{real}. \\ $$ Terms of Service…

Question-59975

Question Number 59975 by vajpaithegrate@gmail.com last updated on 16/May/19 Answered by tanmay last updated on 16/May/19 $${T}.{S}.{A}\:{of}\:{cone}=\pi{rl}+\pi{r}^{\mathrm{2}} \\ $$$$\left.{T}\left..{S}.{A}=\pi{r}\left({r}+\sqrt{{h}^{\mathrm{2}} +{r}^{\mathrm{2}} }\:\right)\:\:\:\:\:\right]\right]{when}\:\left[{l}^{\mathrm{2}} ={r}^{\mathrm{2}} +{h}^{\mathrm{2}} \right] \\…

Question-59974

Question Number 59974 by vajpaithegrate@gmail.com last updated on 16/May/19 Answered by tanmay last updated on 16/May/19 $${lateral}\:{surface}\:{area}=\pi{rl} \\ $$$${given}\:{cos}\mathrm{45}^{{o}} =\frac{{h}}{{l}} \\ $$$${l}=\frac{{h}}{{cos}\mathrm{45}^{{o}} }={h}\sqrt{\mathrm{2}} \\ $$$${tan}\mathrm{45}^{{o}}…