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Category: Differentiation

Question-52945

Question Number 52945 by Tawa1 last updated on 15/Jan/19 Commented by maxmathsup by imad last updated on 15/Jan/19 $$\left.\mathrm{3}\right)\:{let}\:{A}\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}\:{ln}^{\mathrm{2}} \left({x}\right)}{{e}^{{x}} −\mathrm{1}}\:{dx}\:\Rightarrow{A}\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}\:{e}^{−{x}}…

y-log-x-1-x-2-show-that-x-x-1-2-y-2-x-1-2-y-1-2-

Question Number 52820 by 33 last updated on 13/Jan/19 $${y}\:=\:{log}\left\{\sqrt{{x}}\:+\frac{\mathrm{1}}{\:\sqrt{{x}}\:\:\:}\right\}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$${show}\:{that} \\ $$$${x}\left({x}+\mathrm{1}\right)^{\mathrm{2}} {y}_{\mathrm{2}} \:+\:\left({x}+\mathrm{1}\right)^{\mathrm{2}} {y}_{\mathrm{1}} \:=\:\mathrm{2} \\ $$ Answered by tanmay.chaudhury50@gmail.com last…

Advanced-calculus-prove-that-n-1-1-3-n-n-3-7-8-3-1-6-ln-3-2-pi-2-12-ln-2-

Question Number 118304 by mnjuly1970 last updated on 16/Oct/20 $$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\underset{\blacktrinagledown} {\overset{\blacktrinagledown} {\blacklozenge}}\mathscr{A}{dvanced}\:\:{calculus}\underset{\blacktrinagledown} {\overset{\blacktrinagledown} {\blacklozenge}}\:… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{3}^{{n}} {n}^{\mathrm{3}}…

Question-118210

Question Number 118210 by bemath last updated on 16/Oct/20 Answered by john santu last updated on 16/Oct/20 $${Reduces}\:{the}\:{equation}\:{of}\:{the}\:{cylinder} \\ $$$${to}\:{r}^{\mathrm{2}} =\mathrm{2}{r}\:\mathrm{cos}\:\theta\:{or}\:{r}\:=\:\mathrm{2cos}\:\theta,\:{in}\:\theta\:\in\:\left[\mathrm{0},\pi\:\right] \\ $$$${The}\:{volume}\:{equals}\: \\ $$$$\int\int\left(\mathrm{8}{x}^{\mathrm{2}}…

find-value-of-tan46-0-using-calculus-

Question Number 118004 by TANMAY PANACEA last updated on 14/Oct/20 $${find}\:\:{value}\:{of}\:{tan}\mathrm{46}^{\mathrm{0}} \:{using}\:{calculus} \\ $$ Answered by mr W last updated on 14/Oct/20 $$\mathrm{46}°=\mathrm{45}°+\mathrm{1}°=\frac{\pi}{\mathrm{4}}+\frac{\pi}{\mathrm{180}} \\ $$$$\mathrm{tan}\:\mathrm{46}°=\frac{\mathrm{1}+\mathrm{tan}\:\frac{\pi}{\mathrm{180}}}{\mathrm{1}−\mathrm{tan}\:\frac{\pi}{\mathrm{180}}}…

nice-integral-please-prove-0-pi-2-ln-2-cot-x-dx-pi-3-8-m-n-1070-

Question Number 117953 by mnjuly1970 last updated on 14/Oct/20 $$\:\:\:\:\:\:\:\:\:…\:\:\blacktriangleleft{nice}\:\:{integral}\blacktriangleright… \\ $$$$\:\:\:\:{please}\:\:{prove}\:: \\ $$$$ \\ $$$$\:\:\Omega=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {ln}^{\mathrm{2}} \left({cot}\left({x}\right)\right){dx}\:=\frac{\pi^{\mathrm{3}} }{\mathrm{8}}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:…\spadesuit{m}.{n}.\mathrm{1070}\spadesuit… \\ $$ Answered…