Question Number 66790 by mathmax by abdo last updated on 19/Aug/19 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}}{{sh}\left({x}\right)}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 1255 by e.nolley@ieee.org last updated on 18/Jul/15 $$\left(\mathrm{X},\mathrm{F}\left(\mathrm{X}\right)\right),\:\mathrm{X}\in{C},\:\mathrm{F}\left(\mathrm{X}\right)\in{C},\:\:\mathrm{can}\:\mathrm{be}\:\: \\ $$$$\mathrm{plotted}\:\mathrm{in}\:\mathrm{R}^{\mathrm{2}} \:\left(\mathrm{Im}\:\mathrm{on}\:\mathrm{Y},\:\mathrm{Real}\:\mathrm{on}\:\mathrm{X}\right. \\ $$$$\left.\mathrm{axes}\right)\:\mathrm{as}\:\mathrm{a}\:\mathrm{directed}\:\mathrm{line}\:\mathrm{segment}, \\ $$$$\overset{} {\:}\overset{} {\left(\mathrm{X}\right)−−\gg\left(\mathrm{F}\left(\mathrm{X}\right)\right)}.\:\mathrm{This}\:\mathrm{has} \\ $$$$\mathrm{the}\:\mathrm{advantage}\:\mathrm{of}\:\mathrm{showing}\:\mathrm{vector}\: \\ $$$$\mathrm{ffields},\:\mathrm{fixed}\:\mathrm{points}\:\mathrm{and}\:\mathrm{bifurcations}. \\ $$$$…
Question Number 132324 by mnjuly1970 last updated on 13/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:….{advanced}\:\:\:{calculus}… \\ $$$$\:\:\:{evaluation}\:: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}\:^{\:\:} } ^{\:\infty} \frac{{ln}\left(\mathrm{1}+{x}\right)}{{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}\:{dx} \\ $$$$\:\:\:\:{solution}: \\ $$$$\:\:\boldsymbol{\phi}=\left[\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}+{x}\right)}{{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{dx}=\boldsymbol{\phi}_{\mathrm{1}}…
Question Number 66791 by mathmax by abdo last updated on 19/Aug/19 $${let}\:\:{f}\left({x}\right)\:={cos}\left(\mathrm{2}{arctanx}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$ Commented by mathmax by abdo last…
Question Number 132327 by liberty last updated on 13/Feb/21 $$\:\mathrm{If}\:\mathrm{the}\:\mathrm{line}\:\begin{cases}{\frac{\mathrm{x}−\mathrm{1}}{\mathrm{2}}=\frac{\mathrm{y}+\mathrm{1}}{\mathrm{3}}=\frac{\mathrm{z}−\mathrm{1}}{\mathrm{4}}}\\{\frac{\mathrm{x}−\mathrm{3}}{\mathrm{1}}=\frac{\mathrm{y}−\mathrm{k}}{\mathrm{2}}=\frac{\mathrm{z}}{\mathrm{1}}}\end{cases} \\ $$$$\:\mathrm{intersect}\:.\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{is}\: \\ $$ Answered by Ar Brandon last updated on 13/Feb/21 $$\mathrm{L}_{\mathrm{1}} :\:\mathrm{i}−\mathrm{j}+\mathrm{k}+\lambda\left(\mathrm{2i}+\mathrm{3j}+\mathrm{4k}\right)=\left(\mathrm{1}+\mathrm{2}\lambda\right)\mathrm{i}+\left(\mathrm{3}\lambda−\mathrm{1}\right)\mathrm{j}+\left(\mathrm{4}\lambda+\mathrm{1}\right)\mathrm{k} \\…
Question Number 66788 by mathmax by abdo last updated on 19/Aug/19 $${solve}\:{the}\:\left({de}\right)\:\:\:\:\:\left(\mathrm{2}{x}+\mathrm{1}\right){y}^{'} \:\:\:+\left({x}^{\mathrm{2}} −\mathrm{1}\right){y}\:={x}^{\mathrm{3}} {e}^{−{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 66789 by mathmax by abdo last updated on 19/Aug/19 $${sove}\:{the}\:\left({de}\right)\:\:\:\left(\mathrm{1}+\mathrm{2}\sqrt{{x}}\right){y}^{'} −\left({x}+\sqrt{{x}−\mathrm{1}}\right){y}\:={xsin}\left(\mathrm{2}{x}\right) \\ $$ Commented by mathmax by abdo last updated on 20/Aug/19 $$\left({he}\right)\:\rightarrow\left(\mathrm{1}+\mathrm{2}\sqrt{{x}}\right){y}^{'}…
Question Number 132321 by Raxreedoroid last updated on 13/Feb/21 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{cos}\:\left({x}\mathrm{ln}\:{k}\right)}{\left(\mathrm{ln}\:{k}\right)^{{n}} \sqrt{{k}}}=? \\ $$$$\mathrm{where}\:{k},{n}\:\in\mathbb{N}\:,\:{x}\in\mathbb{R} \\ $$ Answered by Dwaipayan Shikari last updated on 13/Feb/21 $$\underset{{n}\rightarrow\infty}…
Question Number 66786 by mathmax by abdo last updated on 19/Aug/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{x}}{{ch}\left({x}\right)}{dx} \\ $$ Commented by mathmax by abdo last updated on 20/Aug/19…
Question Number 1251 by 123456 last updated on 18/Jul/15 $$\mathrm{letsw} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right) \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$$${f}\left({x}\right){f}\left(\frac{\mathrm{1}}{{x}}\right)=\mathrm{1},{x}\neq\mathrm{0} \\ $$$$\mathrm{proof}\:\mathrm{that}\:{f}\left({x}\right)={x}\forall{x}\in\mathbb{R} \\ $$ Commented by prakash jain last…