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 Number 125737 by snipers237 last updated on 13/Dec/20 $$\:{Find}\:{C}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+{e}^{−{u}} }\:{du} \\ $$$${Prove}\:{that}\:\int_{\mathrm{1}} ^{\mathrm{1}+\frac{\mathrm{1}}{{n}}} \sqrt{\mathrm{1}+{x}^{{n}} }\:{dx}\:\underset{\infty} {\sim}\:\frac{{C}}{{n}}\: \\ $$ Answered by MJS_new last…
Question Number 125668 by mnjuly1970 last updated on 12/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:\:{evaluate}::: \\ $$$$\:\:\:\:\:\:\:\:\:\Phi=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} {ln}\left({ln}\left({cot}\left({x}\right)\right)\right){dx}=? \\ $$$$ \\ $$ Answered by mindispower last updated…
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Question Number 59975 by vajpaithegrate@gmail.com last updated on 16/May/19 Answered by tanmay last updated on 16/May/19 $${T}.{S}.{A}\:{of}\:{cone}=\pi{rl}+\pi{r}^{\mathrm{2}} \\ $$$$\left.{T}\left..{S}.{A}=\pi{r}\left({r}+\sqrt{{h}^{\mathrm{2}} +{r}^{\mathrm{2}} }\:\right)\:\:\:\:\:\right]\right]{when}\:\left[{l}^{\mathrm{2}} ={r}^{\mathrm{2}} +{h}^{\mathrm{2}} \right] \\…
Question Number 59974 by vajpaithegrate@gmail.com last updated on 16/May/19 Answered by tanmay last updated on 16/May/19 $${lateral}\:{surface}\:{area}=\pi{rl} \\ $$$${given}\:{cos}\mathrm{45}^{{o}} =\frac{{h}}{{l}} \\ $$$${l}=\frac{{h}}{{cos}\mathrm{45}^{{o}} }={h}\sqrt{\mathrm{2}} \\ $$$${tan}\mathrm{45}^{{o}}…
Question Number 59936 by Sardor2211 last updated on 16/May/19 Answered by tanmay last updated on 16/May/19 $${x}\sqrt{\mathrm{1}+{y}^{\mathrm{2}} }\:+\frac{{dy}}{{dx}}.{y}.\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:=\mathrm{0} \\ $$$${x}\sqrt{\mathrm{1}+{y}^{\mathrm{2}} }\:{dx}+{y}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:{dy}=\mathrm{0} \\ $$$$\frac{{xdx}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 190927 by alcohol last updated on 14/Apr/23 Answered by MikeH last updated on 15/Apr/23 $${I}\:=\:\int{t}^{\mathrm{7}} \mathrm{sin}\left(\mathrm{2}{t}^{\mathrm{4}} \right){dt} \\ $$$$\mathrm{let}\:{u}\:=\mathrm{2}\:{t}^{\mathrm{4}} \:\Rightarrow\:{du}\:=\:\mathrm{8}{t}^{\mathrm{3}} {dt}\:\:\Rightarrow\:{dt}\:=\:\frac{{du}}{\mathrm{8}{t}^{\mathrm{3}} } \\…
Question Number 59838 by necx1 last updated on 15/May/19 $${What}\:{is}\:{the}\:{nth}\:{derivative}\:{of}\:{sinx}\:{in} \\ $$$${terms}\:{of}\:{the}\:{sine}\:{function}? \\ $$ Commented by maxmathsup by imad last updated on 15/May/19 $${if}\:{f}\left({x}\right)={sinx}\:\:\:,\:\:{f}^{\left({n}\right)} \left({x}\right)\:={sin}\left({x}+\frac{{n}\pi}{\mathrm{2}}\right)\:\:\:{with}\:{n}\geqslant\mathrm{1}\:\:{and}\:\:{f}^{\left(\mathrm{0}\right)}…