Question Number 61536 by maxmathsup by imad last updated on 04/Jun/19 $$\left.\mathrm{1}\right){let}\:{U}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \left(−\mathrm{1}\right)^{{k}} \:=\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+…\left({n}+\mathrm{1}\:{terms}\right) \\ $$$${is}\:{lim}_{{n}\rightarrow+\infty} {U}_{{n}} {exist}\:?\:\:{find}\:{U}_{{n}} \:{by}\:{using}\:{integr}\:{part}\left[..\right] \\ $$$$\left.\mathrm{2}\right)\:{let}\:{V}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}}…
Question Number 61535 by maxmathsup by imad last updated on 04/Jun/19 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{ln}\left(\mathrm{1}+{cosx}\right)}{{cosx}}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 192604 by sciencestudentW last updated on 22/May/23 $${many}\:{people}\:{say}\:{that}\:{the}\:\mathrm{0}^{\mathrm{0}\:} {is}\:{an}\:{uninfinity} \\ $$$${ones}\:{of}\:{them}\:{say}\:{that}\:\mathrm{0}^{\mathrm{0}} \:{is}\:{infinity}\:{and}\:{equal}\:{to}\:\mathrm{1}! \\ $$$${what}\:{do}\:{you}\:{think}\:{wich}\:{ones}\:{of}\:{them} \\ $$$${say}\:{right}? \\ $$ Commented by Frix last updated…
Question Number 61534 by maxmathsup by imad last updated on 04/Jun/19 $${calculate}\:{f}\left({a}\right)\:=\int\int_{{W}} \:\left({x}+{ay}\right){e}^{−{x}} \:{e}^{−{ay}} {dxdy}\:{with} \\ $$$${W}_{{a}} =\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /{x}\geqslant\mathrm{0}\:,{y}\geqslant\mathrm{0}\:\:\:,\:{x}+{ay}\:\leqslant\mathrm{1}\:\right\}\:\:\:{a}>\mathrm{0} \\ $$ Terms of Service Privacy…
Question Number 61533 by maxmathsup by imad last updated on 04/Jun/19 $$\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\:\:\frac{{x}−{y}}{\left({x}^{\mathrm{2}} \:+\mathrm{3}{y}^{\mathrm{2}\:} \:+\mathrm{1}\right)^{\mathrm{2}} }\:{dxdy}\: \\ $$ Commented by maxmathsup by imad last…
Question Number 192606 by sciencestudentW last updated on 22/May/23 $${proof}\:{that}\:\mathrm{0}^{\mathrm{0}} =\mathrm{1}\:{without}\:{limit}! \\ $$ Commented by Frix last updated on 22/May/23 $$\mathrm{There}'\mathrm{s}\:\mathrm{no}\:\mathrm{proof}\:\mathrm{as}\:\mathrm{it}'\mathrm{s}\:\mathrm{a}\:\mathrm{matter}\:\mathrm{of} \\ $$$$\mathrm{definition}.\:\mathrm{I}\:\mathrm{tried}\:\mathrm{to}\:\mathrm{explain}\:\mathrm{but}\:\mathrm{maybe} \\ $$$$\mathrm{you}\:\mathrm{need}\:\mathrm{to}\:\mathrm{learn}\:\mathrm{more}\:\mathrm{before}\:\mathrm{you}\:\mathrm{can}…
Question Number 61532 by maxmathsup by imad last updated on 04/Jun/19 $${prove}\:{that}\:\:\:\frac{\left({a}+{b}\right)^{{n}} }{{a}^{{n}} \:+{b}^{{n}} }\:<\mathrm{2}^{{n}−\mathrm{1}} \:\:\:\:\:\forall\:{n}>\mathrm{1}\:\:\:\:\left({n}\:{natural}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 127067 by benjo_mathlover last updated on 26/Dec/20 $$\:{If}\:\begin{cases}{\mathrm{sin}\:{x}+\mathrm{sin}\:\mathrm{2}{x}\:=\:{a}}\\{\mathrm{cos}\:{x}+\mathrm{cos}\:\mathrm{2}{x}\:=\:{b}\:}\end{cases} \\ $$$${show}\:{that}\:\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} −\mathrm{3}\right)=\mathrm{2}{b}. \\ $$ Answered by liberty last updated on 26/Dec/20…
Question Number 61530 by maxmathsup by imad last updated on 04/Jun/19 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{x}^{−\mathrm{2}{n}} }{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx}\:\:\:{with}\:{n}\:{integr}\:{natural}\:{and}\:\:\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{n}^{\mathrm{2}} \:{U}_{{n}} \\…
Question Number 127064 by benjo_mathlover last updated on 26/Dec/20 $$\:\:\:\left({D}^{\mathrm{2}} −\mathrm{1}\right){y}\:=\:{x}\:\mathrm{sin}\:{x}\: \\ $$ Answered by liberty last updated on 26/Dec/20 $$\:{The}\:{characteristic}\:{eq}\:{of}\:\left({D}^{\mathrm{2}} −\mathrm{1}\right){y}\:=\:\mathrm{0} \\ $$$${is}\:\lambda^{\mathrm{2}} −\mathrm{1}=\mathrm{0}\:,\:{has}\:{the}\:{roots}\:\lambda=\pm\mathrm{1}…