Question Number 65651 by Masumsiddiqui399@gmail.com last updated on 01/Aug/19 Commented by Prithwish sen last updated on 01/Aug/19 $$\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{0}\:\Rightarrow\mathrm{x}−\mathrm{1}=\mathrm{0}\:\mathrm{and}\:\mathrm{y}=\mathrm{0} \\ $$$$\therefore\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} =\mathrm{1} \\…
Question Number 131132 by 676597498 last updated on 01/Feb/21 $$\mathrm{u}\left(\mathrm{x}\right)=\mathrm{cosh}\left(\mathrm{x}\right)−\mathrm{x} \\ $$$$\mathrm{v}_{\mathrm{n}+\mathrm{1}} =\mathrm{u}\left(\mathrm{v}_{\mathrm{n}} \right) \\ $$$$\mathrm{m}=\sqrt{\mathrm{2}}−\mathrm{ln}\left(\mathrm{1}+\sqrt{\mathrm{2}}\right) \\ $$$$\mathrm{v}_{\mathrm{0}} =\mathrm{1} \\ $$$$\mathrm{A}.\:\mathrm{V}_{\mathrm{n}} −\mathrm{V}_{\mathrm{0}} =\mathrm{nm} \\ $$$$\mathrm{B}.\:\mathrm{v}_{\mathrm{n}}…
Question Number 131121 by abdurehime last updated on 01/Feb/21 Answered by mathmax by abdo last updated on 01/Feb/21 $$\left.\mathrm{A}\right)\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\mathrm{25}\:\Rightarrow\mathrm{y}^{\mathrm{2}} \:=\mathrm{25}−\mathrm{x}^{\mathrm{2}} \:\Rightarrow\mathrm{y}=\xi\sqrt{\mathrm{25}−\mathrm{x}^{\mathrm{2}} }\left(\:\xi=\overset{−} {+}\mathrm{1}\right)\:\Rightarrow…
Question Number 131104 by mnjuly1970 last updated on 01/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{x}^{{b}−\mathrm{1}} }{\left(\mathrm{1}+{x}^{{a}} \right)^{{s}} }{dx}\overset{???} {=}\frac{\Gamma\left(\frac{{b}}{{a}}\right)\Gamma\left({s}−\frac{{b}}{{a}}\right)}{{a}\Gamma\left({s}\right)} \\ $$ Answered by Ar Brandon last…
Question Number 29 by user1 last updated on 25/Jan/15 $$\mathrm{Differentiate}\:\:\:{e}^{\sqrt{\mathrm{cot}\:{x}}} . \\ $$ Answered by user2 last updated on 03/Nov/14 $$\mathrm{Let}\:\:\:{y}={e}^{\sqrt{\mathrm{cot}\:{x}}} \\ $$$$\mathrm{Put}\:\mathrm{cot}\:{x}\:={t}\:\mathrm{and}\:\sqrt{\mathrm{cot}\:{x}}=\sqrt{{t}}={u},\:\mathrm{so}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}={e}^{{u}}…
Question Number 131103 by mnjuly1970 last updated on 01/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:{prove}\:\:{that}\::: \\ $$$$\:\:\underset{{n}\in\mathbb{N}} {\sum}\left(\frac{\Gamma^{\mathrm{2}} \left({n}\right)}{\mathrm{2}^{−{n}} \left(\mathrm{2}{n}−\mathrm{1}\right)!}\right)=\pi \\ $$$$ \\ $$ Answered by Ar Brandon…
Question Number 78526 by TawaTawa last updated on 18/Jan/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\left[\frac{\int_{\:\:\mathrm{0}} ^{\:\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \:\sqrt{\mathrm{4}\:+\:\boldsymbol{\mathrm{t}}^{\mathrm{3}} }\:\:\boldsymbol{\mathrm{dt}}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\right] \\ $$ Commented by mr W last updated on…
Question Number 12968 by @ANTARES_VY last updated on 08/May/17 $$\left(\boldsymbol{\mathrm{x}}+\mathrm{3}\right)^{\mathrm{2}} +\left(\boldsymbol{\mathrm{y}}−\mathrm{5}\right)^{\mathrm{2}} =\mathrm{45}\:\:\:\boldsymbol{\mathrm{A}}\left(\mathrm{0};\mathrm{11}\right) \\ $$$$\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{circle}}\:\:\boldsymbol{\mathrm{to}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{point}}\:\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{trying}}\:\:\boldsymbol{\mathrm{to}}\:\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{angular}}\:\:\boldsymbol{\mathrm{coefficient}}. \\ $$ Answered by 433 last updated on 08/May/17…
Question Number 78490 by ~blr237~ last updated on 18/Jan/20 $$\mathrm{Find}\:\mathrm{out}\:\mathrm{A}\:=\underset{\mathrm{n}=\mathrm{2}} {\overset{\infty} {\sum}}\:\:\frac{\zeta\left(\mathrm{n}\right)}{\mathrm{n}\left(−\mathrm{3}\right)^{\mathrm{n}} }\:\:\:\:\:\:\:\:\:\:\:\mathrm{where}\:\:\zeta\left(\mathrm{p}\right)=\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{p}} }\: \\ $$ Answered by mind is power last updated…
Question Number 78489 by ~blr237~ last updated on 18/Jan/20 $$\mathrm{let}\:\:\mathrm{P}\left(\mathrm{x}\right)=\:\mathrm{x}^{\mathrm{5}} −\mathrm{209x}+\mathrm{56}\: \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{two}\:\mathrm{roots}\:\:\mathrm{a},\mathrm{b}\:\mathrm{such}\:\mathrm{as}\:\:\:\mathrm{ab}=\mathrm{1} \\ $$$$\mathrm{Find}\:\mathrm{out}\:\mathrm{their}\:\mathrm{sum}\:\left(\:\mathrm{a}+\mathrm{b}=?\right)\:\:\mathrm{and}\:\mathrm{deduce}\:\mathrm{the}\:\mathrm{decomposition}\:\mathrm{of}\:\mathrm{P}\left(\mathrm{x}\right)\:\mathrm{in}\:\mathrm{prime}\:\mathrm{factors}. \\ $$ Answered by MJS last updated on 18/Jan/20 $$\mathrm{2}\:\mathrm{roots}\:\mathrm{with}\:{ab}=\mathrm{1}\:\Rightarrow\:\mathrm{we}\:\mathrm{have}\:\mathrm{a}\:\mathrm{square}\:\mathrm{factor}…