Question Number 25488 by Mahesh Andiboina last updated on 11/Dec/17 Commented by prakash jain last updated on 11/Dec/17 $${xy}=\mathrm{1} \\ $$$$\Rightarrow{y}=\frac{\mathrm{1}}{{x}} \\ $$$$\frac{{dy}}{{dx}}=−\frac{\mathrm{1}}{{x}^{\mathrm{2}} } \\…
Question Number 91000 by niroj last updated on 27/Apr/20 $$\:\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equations}}: \\ $$$$\:\:\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }+\:\frac{\boldsymbol{\mathrm{x}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}−\:\frac{\boldsymbol{\mathrm{y}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }=\:\boldsymbol{\mathrm{x}}\sqrt{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \\ $$ Commented by niroj last updated on…
Question Number 90881 by M±th+et+s last updated on 26/Apr/20 $${if}\:{the}\:{value}\:{of}\:{x}\:{is}\:{in}\:{degrees}\:{what}\:{is} \\ $$$${the}\:{derivative}\:{of}\:\:\:{f}\left({x}\right)={sin}\left({x}\right) \\ $$ Commented by mr W last updated on 28/Apr/20 $${we}\:{have}\:{different}\:{understanding}: \\ $$$${if}\:{x}\:{is}\:{in}\:{rad},\:{the}\:{slope}\:\frac{{dy}}{{dx}}\:{is}\:{in}\:{unit}…
Question Number 156386 by mnjuly1970 last updated on 10/Oct/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\phi\:\left({n}\:\right)=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\:\right)^{\:{k}−\mathrm{1}} \begin{pmatrix}{\:{n}}\\{\:{k}}\end{pmatrix}\:\mathrm{H}_{\:{k}} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{Find}\:\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left(−\mathrm{1}\right)^{\:{n}−\mathrm{1}} \:\phi\:\left(\:{n}^{\:\mathrm{2}} \right)\:=? \\ $$…
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} \\…