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…
Question Number 66787 by mathmax by abdo last updated on 19/Aug/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{x}^{\mathrm{2}} }{{ch}\left({x}\right)}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 66778 by Tony Lin last updated on 19/Aug/19 $$\frac{\mathrm{1}}{\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{2}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}}−\frac{\mathrm{2}}{\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{7}}+\frac{\mathrm{1}}{\mathrm{8}}−\frac{\mathrm{2}}{\mathrm{9}}+\frac{\mathrm{1}}{\mathrm{10}}+\frac{\mathrm{1}}{\mathrm{11}}−\frac{\mathrm{2}}{\mathrm{12}}+\centerdot\centerdot\centerdot= \\ $$ Commented by Prithwish sen last updated on 19/Aug/19 $$\left(\frac{\mathrm{1}}{\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+……\right)−\left[\left(\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{3}}\right)+\left(\frac{\mathrm{1}}{\mathrm{6}}+\frac{\mathrm{2}}{\mathrm{6}}\right)+\left(\frac{\mathrm{1}}{\mathrm{9}}+\frac{\mathrm{2}}{\mathrm{9}}\right)+\left(\frac{\mathrm{1}}{\mathrm{12}}+\frac{\mathrm{2}}{\mathrm{12}}\right)+…\right] \\ $$$$=\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty}…
Question Number 1239 by Rasheed Ahmad last updated on 17/Jul/15 $${Rasheed}\:{Ahmad}\:\left({Rasheed}\:{Soomro}\right) \\ $$$$\bullet\mathrm{For}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{where}\:\mathrm{x}\:\mathrm{and}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{both}\:{are} \\ $$$$\mathrm{real}\:\mathrm{the}\:\left(\mathrm{x},{f}\left({x}\right)\right)\:{can}\:{be}\:{plotted}\:{as} \\ $$$${a}\:{point}\:{easily}.\:\bullet{Now}\:{consider}\:{F}\left({X}\right) \\ $$$${where}\:{X}\:{and}\:{F}\left({X}\right)\:{are}\:{complex}\: \\ $$$${numbers}.\:{How}\:{can}\:\left({X},{F}\left({X}\right)\right)\:{be} \\ $$$${plotted}?\:{For}\:{a}\:{particular}\:{example}:\:\left(\mathrm{3}+\mathrm{2}{i},\mathrm{4}−\mathrm{5}{i}\right) \\ $$$${how}\:{can}\:{be}\:{plotted}?…
Question Number 66768 by John Kaloki Musau last updated on 19/Aug/19 $${without}\:{using}\:{mathematical}\:{tables} \\ $$$${evaluate} \\ $$$$\frac{\mathrm{sin}\:\mathrm{60}.\mathrm{tan}\:\mathrm{30}.\mathrm{cos}\:\mathrm{60}+\mathrm{sin}\:\mathrm{30}.\mathrm{cos}\:\mathrm{45}.\mathrm{sin}\:\mathrm{45}}{\mathrm{sin}\:\mathrm{90}.\mathrm{cos}\:\mathrm{45}.\mathrm{sin}\:\mathrm{45}−\mathrm{sin}\:\mathrm{60}.\mathrm{cos}\:\mathrm{30}.\mathrm{sin}\:\mathrm{30}} \\ $$ Commented by Tony Lin last updated on…
Question Number 66769 by John Kaloki Musau last updated on 19/Aug/19 $${simplify} \\ $$$$\frac{{x}+\mathrm{4}}{{x}−\mathrm{4}}−\frac{\mathrm{5}{x}+\mathrm{20}}{{x}^{\mathrm{2}} −\mathrm{16}} \\ $$ Commented by Prithwish sen last updated on 19/Aug/19…