Question Number 146898 by mathmax by abdo last updated on 16/Jul/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{cosx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}\right)}\mathrm{dx} \\ $$ Answered by qaz last updated on…
Question Number 81195 by jagoll last updated on 10/Feb/20 $${what}\:{is}\:{asymtote}\:{og}\:{function} \\ $$$${y}^{\mathrm{2}} \left({x}−\mathrm{2}{a}\right)={x}^{\mathrm{3}} −{a}^{\mathrm{3}} \:? \\ $$ Commented by mr W last updated on 10/Feb/20…
Question Number 146705 by mathmax by abdo last updated on 15/Jul/21 $$\mathrm{find}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{sin}\left(\mathrm{tan}\left(\mathrm{2x}\right)−\mathrm{x}\right)+\mathrm{1}−\mathrm{cos}\left(\pi\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{2}} } \\ $$ Answered by Olaf_Thorendsen last updated on 15/Jul/21 $${f}\left({x}\right)\:=\:\frac{\mathrm{sin}\left(\mathrm{tan}\left(\mathrm{2}{x}\right)−{x}\right)+\mathrm{1}−\mathrm{cos}\left(\pi{x}\right)}{{x}^{\mathrm{2}}…
Question Number 81027 by abdomathmax last updated on 09/Feb/20 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{tan}\left(\mathrm{2}{x}\right)−\mathrm{2}{tanx}−\mathrm{2}{tan}^{\mathrm{3}} {x}}{{x}^{\mathrm{5}} } \\ $$ Commented by john santu last updated on 09/Feb/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{tan2}{x}\:}{\mathrm{2}{x}}.\left(\mathrm{2}{x}\right)−\frac{\mathrm{2tan}\:{x}}{{x}}.\left({x}\right)−\frac{\mathrm{2tan}^{\mathrm{3}}…
Question Number 146549 by mathmax by abdo last updated on 13/Jul/21 $$\mathrm{find}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{cos}\left(\mathrm{x}−\mathrm{sinx}\right)+\mathrm{1}−\mathrm{cos}\left(\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{2}} } \\ $$ Answered by Olaf_Thorendsen last updated on 14/Jul/21 $$\frac{\mathrm{cos}\left({x}−\mathrm{sin}{x}\right)+\mathrm{1}−\mathrm{cos}\left({x}^{\mathrm{2}}…
Question Number 146550 by mathmax by abdo last updated on 13/Jul/21 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{3}} \:\mathrm{arctan}\left(\frac{\mathrm{2}}{\mathrm{x}}\right) \\ $$$$\left.\mathrm{1}\right)\mathrm{calculate}\:\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{srie}\:\mathrm{at}\:\mathrm{x}_{\mathrm{0}} =\mathrm{1} \\ $$ Terms of Service Privacy…
Question Number 146548 by mathmax by abdo last updated on 13/Jul/21 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{cos}\left(\alpha\mathrm{x}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie}\:\:\left(\alpha\:\mathrm{real}\right) \\ $$ Answered by Olaf_Thorendsen last updated on 14/Jul/21 $${a}_{\mathrm{0}} \:=\:\frac{\mathrm{1}}{\mathrm{T}}\int_{−\frac{\mathrm{T}}{\mathrm{2}}} ^{+\frac{\mathrm{T}}{\mathrm{2}}} {f}\left({x}\right){dx}…
Question Number 146547 by mathmax by abdo last updated on 13/Jul/21 $$\mathrm{calculate}\:\int_{\mid\mathrm{z}\mid=\mathrm{5}} \:\:\:\frac{\mathrm{2}−\mathrm{z}^{\mathrm{2}} }{\left(\mathrm{z}^{\mathrm{2}} +\mathrm{9}\right)\left(\mathrm{z}−\mathrm{i}\right)^{\mathrm{2}} }\mathrm{dz} \\ $$ Answered by Olaf_Thorendsen last updated on 14/Jul/21…
Question Number 146546 by mathmax by abdo last updated on 13/Jul/21 $$\mathrm{find}\:\int_{\mid\mathrm{z}−\mathrm{1}\mid=\mathrm{3}} \:\:\frac{\mathrm{cos}\left(\pi\mathrm{z}\right)}{\left(\mathrm{z}−\mathrm{2}\right)\left(\mathrm{z}^{\mathrm{2}} +\mathrm{4}\right)}\mathrm{dz} \\ $$ Answered by Olaf_Thorendsen last updated on 14/Jul/21 $${f}\left({z}\right)\:=\:\frac{\mathrm{cos}\left(\pi{z}\right)}{\left({z}−\mathrm{2}\right)\left({z}^{\mathrm{2}} +\mathrm{4}\right)}…
Question Number 15463 by myintkhaing last updated on 10/Jun/17 $${Find}\:{the}\:{domain}\:{and}\:{range}\:{of}\:{a}\:{function}\:{for}\:{which}\:{f}\left({x}\right)=\frac{\mathrm{1}+\mathrm{2}{x}}{{x}}. \\ $$ Answered by Tinkutara last updated on 10/Jun/17 $${f}\left({x}\right)\:\mathrm{is}\:\mathrm{defined}\:\forall\:{x}\:\in\:{R}\:−\:\left\{\mathrm{0}\right\}. \\ $$$$\mathrm{Domain}\:=\:{R}\:−\:\left\{\mathrm{0}\right\} \\ $$$$\mathrm{Let}\:{y}\:=\:\frac{\mathrm{2}{x}\:+\:\mathrm{1}}{{x}} \\…