Question Number 17359 by ajfour last updated on 04/Jul/17 $$\mathrm{For}\:\mathrm{what}\:\mathrm{values}\:\mathrm{of}\:\mathrm{m},\:\mathrm{the}\:\mathrm{equation} \\ $$$$\left(\mathrm{1}+\mathrm{m}\right)\mathrm{x}^{\mathrm{2}} −\mathrm{2}\left(\mathrm{1}+\mathrm{3m}\right)\mathrm{x}+\left(\mathrm{1}+\mathrm{8m}\right)=\mathrm{0}\:; \\ $$$$\:\:\:\mathrm{m}\:\in\:\mathrm{R}\:,\:\mathrm{has}\:\mathrm{both}\:\mathrm{roots}\:\mathrm{positive}\:? \\ $$ Commented by ajfour last updated on 04/Jul/17 $$\mathrm{book}'\mathrm{s}\:\mathrm{answer}:…
Question Number 17354 by ajfour last updated on 04/Jul/17 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:: \\ $$$$\mid\mathrm{x}−\mathrm{1}\mid−\mid\mathrm{x}−\mathrm{2}\mid+\mid\mathrm{x}+\mathrm{1}\mid>\mid\mathrm{x}+\mathrm{2}\mid+\mid\mathrm{x}\mid−\mathrm{3}\:. \\ $$ Commented by ajfour last updated on 04/Jul/17 $$\mathrm{my}\:\mathrm{answer}:\:\mathrm{x}\in\:\left(−\mathrm{3},\:\mathrm{3}\right)−\left\{−\mathrm{1},\:\mathrm{1}\:\right\} \\ $$$$\mathrm{answer}\:\mathrm{in}\:\mathrm{book}:\:\:\mathrm{x}\in\:\left(\mathrm{1},\:\mathrm{3}\right)\:. \\…
Question Number 148372 by mathmax by abdo last updated on 27/Jul/21 $$\mathrm{calculate}\:\int_{\gamma} \mathrm{z}^{\mathrm{3}} \:\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{2}} }} \mathrm{dz}\:\:\mathrm{with}\:\gamma\left(\mathrm{t}\right)=\mathrm{3e}^{\mathrm{it}} \:\:\:\:\mathrm{and}\:\mathrm{t}\in\left[\mathrm{0},\mathrm{2}\pi\right] \\ $$ Answered by mathmax by abdo last…
Question Number 148371 by mathmax by abdo last updated on 27/Jul/21 $$\mathrm{calculate}\:\int_{\gamma} \mathrm{ze}^{\frac{\mathrm{2}}{\mathrm{z}^{\mathrm{2}} }} \mathrm{dz}\:\:\:\mathrm{with}\:\gamma\left(\mathrm{t}\right)=\sqrt{\mathrm{3}}\mathrm{e}^{\mathrm{it}} \:\:\:\:\:\:\mathrm{t}\in\left[\mathrm{0},\mathrm{2}\pi\right] \\ $$ Answered by mathmax by abdo last updated…
Question Number 148303 by mathmax by abdo last updated on 26/Jul/21 $$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{cos}\left(\mathrm{2x}\right)}{\mathrm{sin}\left(\mathrm{x}\right)} \\ $$$$\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by Olaf_Thorendsen last updated on 27/Jul/21 $${f}\left({x}\right)\:=\:\frac{\mathrm{cos}\left(\mathrm{2}{x}\right)}{\mathrm{sin}{x}} \\…
Question Number 148302 by mathmax by abdo last updated on 26/Jul/21 $$\mathrm{calculate}\:\:\int_{\mid\mathrm{z}\mid=\mathrm{3}} \:\:\:\frac{\mathrm{cos}\left(\mathrm{2iz}\right)}{\left(\mathrm{z}−\mathrm{2i}\right)\left(\mathrm{z}+\mathrm{i}\sqrt{\mathrm{3}}\right)^{\mathrm{2}} }\mathrm{dz} \\ $$ Answered by Olaf_Thorendsen last updated on 27/Jul/21 $${f}\left({z}\right)\:=\:\frac{\mathrm{cos}\left(\mathrm{2}{iz}\right)}{\left({z}−\mathrm{2}{i}\right)\left({z}+{i}\sqrt{\mathrm{3}}\right)^{\mathrm{2}} }…
Question Number 82719 by john santu last updated on 23/Feb/20 $$\mathrm{If}\:\mathrm{x},{y}\:\in\mathbb{R}\:{satisfy}\:{in}\:{equation}\: \\ $$$${x}−\mathrm{4}\sqrt{{y}}\:=\:\mathrm{2}\sqrt{{x}−{y}}\:.\:{find}\:{range}\:{of}\:{x} \\ $$ Commented by MJS last updated on 23/Feb/20 $$\mathrm{4}\leqslant{x}\leqslant\mathrm{20} \\ $$$$\mathrm{I}\:\mathrm{will}\:\mathrm{show}\:\mathrm{later}…
Question Number 148237 by puissant last updated on 26/Jul/21 $${f}\left({t}\right)={sin}\left({pt}\right)\:{fourier}\:{serie}.. \\ $$ Answered by Olaf_Thorendsen last updated on 26/Jul/21 $${f}\:\mathrm{est}\:\mathrm{une}\:\mathrm{fonction}\:\mathrm{impaire}\:\mathrm{et}\: \\ $$$$\mathrm{donc}\:{a}_{\mathrm{0}} \:=\:\mathrm{0}.\:\mathrm{Les}\:\mathrm{autres}\:{a}_{{n}} \mathrm{sont}\:\mathrm{nuls} \\…
Question Number 148213 by mathmax by abdo last updated on 26/Jul/21 $$\mathrm{f}\left(\mathrm{z}\right)=\frac{\mathrm{cosz}}{\mathrm{1}−\mathrm{sin}\left(\mathrm{z}^{\mathrm{2}} \right)} \\ $$$$\mathrm{find}\:\mathrm{residus}\:\mathrm{of}\:\mathrm{f} \\ $$ Answered by puissant last updated on 26/Jul/21 $$\mathrm{sin}\left(\mathrm{z}^{\mathrm{2}}…
Question Number 17093 by 1234Hello last updated on 02/Jul/17 $$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{function} \\ $$$$\mathrm{satisfying}\:{f}\left({x}\right).{f}\left(\frac{\mathrm{1}}{{x}}\right)\:=\:{f}\left({x}\right)\:+\:{f}\left(\frac{\mathrm{1}}{{x}}\right)\:; \\ $$$${x}\:\in\:{R}\:−\:\left\{\mathrm{0}\right\}\:\mathrm{and}\:{f}\left(\mathrm{3}\right)\:=\:\mathrm{28},\:\mathrm{then}\:{f}\left(\mathrm{4}\right)\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to} \\ $$ Commented by prakash jain last updated on…