Question Number 156386 by mnjuly1970 last updated on 10/Oct/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\phi\:\left({n}\:\right)=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\:\right)^{\:{k}−\mathrm{1}} \begin{pmatrix}{\:{n}}\\{\:{k}}\end{pmatrix}\:\mathrm{H}_{\:{k}} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{Find}\:\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left(−\mathrm{1}\right)^{\:{n}−\mathrm{1}} \:\phi\:\left(\:{n}^{\:\mathrm{2}} \right)\:=? \\ $$…
Question Number 90783 by john santu last updated on 26/Apr/20 $${can}\:{inflection}\:{point}\: \\ $$$${be}\:{a}\:{max}\:{or}\:{min}\:?\: \\ $$ Commented by jagoll last updated on 26/Apr/20 $${given}\:{a}\:{curve}\:{y}\:=\:{f}\left({x}\right)\:.\:{a}\:{point}\: \\ $$$$\left({x}_{\mathrm{1}}…
Question Number 25229 by NECx last updated on 06/Dec/17 $$\int\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{dx} \\ $$ Commented by prakash jain last updated on 06/Dec/17 $${x}=\mathrm{sinh}\:{u} \\ $$$${dx}=\mathrm{cosh}\:{u}\centerdot{du} \\…
Question Number 90730 by ~blr237~ last updated on 25/Apr/20 $${let}\:{a}\:,{b}\:{integer}\:{and}\:\:{C}={a}^{\mathrm{2}} +{b}^{\mathrm{2}} \: \\ $$$${Prove}\:{that}\:{there}\:{exist}\:{a}_{{n}} \:{and}\:{b}_{{n}} \:{all}\: \\ $$$${integers}\:{such}\:{as}\:{C}^{{n}} ={a}_{{n}} ^{\mathrm{2}} \:+{b}_{{n}} ^{\mathrm{2}} \: \\ $$$${explicit}\:{a}_{\mathrm{5}}…
Question Number 90727 by ~blr237~ last updated on 25/Apr/20 $$\underset{{a},{b}\geqslant\mathrm{1}} {\sum}\:\frac{\mathrm{1}}{\left({a}+{b}^{\mathrm{2}} \right)\left({a}+{b}^{\mathrm{2}} +\mathrm{1}\right)}\:\:\:\:\:\:{nature}\:{and}\:\:{sum}\:{value}\:\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 90679 by MWSuSon last updated on 25/Apr/20 $${if}\:{y}={sin}\left({m}\mathrm{sin}^{−\mathrm{1}} {x}\right),\:{prove}\:{that}\:\left(\mathrm{1}−{x}^{\mathrm{2}} \right){y}_{{n}+\mathrm{2}} −\left(\mathrm{2}{n}+\mathrm{1}\right){xy}_{{n}+\mathrm{1}} +\left({m}^{\mathrm{2}} −{n}^{\mathrm{2}} \right){y}_{{n}} =\mathrm{0} \\ $$ Commented by MWSuSon last updated on…
Question Number 156206 by mnjuly1970 last updated on 09/Oct/21 $$ \\ $$$$\Omega\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \sqrt{{x}}\:\sqrt{\mathrm{1}−\sqrt{{x}}\:}\:\sqrt{\mathrm{1}−\sqrt{\mathrm{1}−\sqrt{{x}}\:}}\:{dx}=? \\ $$ Answered by mindispower last updated on 09/Oct/21 $$\sqrt{\mathrm{1}−\sqrt{{x}}}={u} \\…
Question Number 90630 by jagoll last updated on 25/Apr/20 $${f}\left({x}\right)\:=\:{xe}^{−{x}} \\ $$$${f}^{\left(\mathrm{2020}\right)} \left({x}\right)\:=\: \\ $$ Commented by john santu last updated on 25/Apr/20 $${f}^{\left({n}\right)} \left({x}\right)\:=\:\begin{cases}{\left({n}−{x}\right).{e}^{−{x}}…
Question Number 156137 by cortano last updated on 08/Oct/21 Answered by mr W last updated on 09/Oct/21 Commented by mr W last updated on 09/Oct/21…
Question Number 90575 by niroj last updated on 24/Apr/20 $$\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{y}}_{\mathrm{3}} +\left(\mathrm{1}−\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)\boldsymbol{\mathrm{y}}_{\mathrm{2}} −\mathrm{8}\boldsymbol{\mathrm{x}}\:_{\:} \boldsymbol{\mathrm{y}}_{\mathrm{1}} −\mathrm{4}\boldsymbol{\mathrm{y}}=\:\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} \\ $$ Terms of Service Privacy Policy Contact:…