Question Number 96658 by mathmax by abdo last updated on 03/Jun/20 $$\mathrm{determine}\:\mathrm{L}\left(\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} −\mathrm{x}} \right)\:\:\:\mathrm{with}\:\mathrm{L}\:\mathrm{laplace}\:\mathrm{transform} \\ $$ Answered by mathmax by abdo last updated on 04/Jun/20…
Question Number 96657 by mathmax by abdo last updated on 03/Jun/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{e}^{−\mathrm{x}} \:,\:\:\mathrm{2}\pi\:\mathrm{periodic}\:\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by mathmax by abdo last updated on 04/Jun/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\sum_{\mathrm{n}=−\infty}…
Question Number 96656 by mathmax by abdo last updated on 03/Jun/20 $$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)\:=\frac{\mathrm{2}}{\mathrm{cosx}}\:\:\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by mathmax by abdo last updated on 04/Jun/20 $$\mathrm{we}\:\mathrm{have}\:\mathrm{g}\left(\mathrm{x}\right)\:=\frac{\mathrm{2}}{\mathrm{cosx}}\:\Rightarrow\mathrm{g}\left(\mathrm{x}\right)\:=\frac{\mathrm{4}}{\mathrm{e}^{\mathrm{ix}} \:+\mathrm{e}^{−\mathrm{ix}}…
Question Number 96655 by mathmax by abdo last updated on 03/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{ln}\left(\mathrm{2}+\mathrm{cosx}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by mathmax by abdo last updated on 04/Jun/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{ln}\left(\mathrm{2}+\mathrm{cosx}\right)\:\Rightarrow\mathrm{f}^{'} \left(\mathrm{x}\right)\:=\frac{−\mathrm{sinx}}{\mathrm{2}+\mathrm{cosx}}\:=−\frac{\frac{\mathrm{e}^{\mathrm{ix}}…
Question Number 96607 by bemath last updated on 03/Jun/20 $$\mathrm{It}\:\mathrm{is}\:\mathrm{given}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{function} \\ $$$$\mathrm{defined}\:\mathrm{on}\:\mathbb{R},\:\mathrm{satisfying}\:\mathrm{f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{for}\:\mathrm{any}\:\mathrm{x}\in\mathbb{R},\:\mathrm{f}\left(\mathrm{x}+\mathrm{5}\right)\:\geqslant\mathrm{f}\left(\mathrm{x}\right)+\mathrm{5} \\ $$$$\mathrm{and}\:\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)\:\leqslant\mathrm{f}\left(\mathrm{x}\right)+\mathrm{1}.\:\mathrm{If}\:\mathrm{g}\left(\mathrm{x}\right)= \\ $$$$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{1}−\mathrm{x},\:\mathrm{then}\:\mathrm{g}\left(\mathrm{2002}\right)\:=\:\_\_\_ \\ $$ Commented by bobhans last updated…
Question Number 96593 by mathmax by abdo last updated on 03/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{arctan}\left(\mathrm{x}^{\mathrm{n}} \right)\:\mathrm{with}\:\mathrm{n}\:\mathrm{integr}\:\mathrm{natural} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{'} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{2}\right)} \left(\mathrm{x}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$…
Question Number 96570 by mathmax by abdo last updated on 02/Jun/20 $$\mathrm{solve}\:\:\mathrm{xy}^{''} \:−\left(\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)\mathrm{y}^{'} \:+\mathrm{2y}\:=\mathrm{x}^{\mathrm{2}} \:\mathrm{e}^{−\mathrm{x}} \:\mathrm{with}\:\:\mathrm{y}\left(\mathrm{o}\right)=\mathrm{1}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)=−\mathrm{2} \\ $$ Terms of Service Privacy Policy…
Question Number 96571 by mathmax by abdo last updated on 02/Jun/20 $$\mathrm{solve}\:\mathrm{y}^{''} −\mathrm{2y}^{'} \:+\mathrm{y}\:=\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \:\mathrm{e}^{−\mathrm{x}} \:\mathrm{with}\:\mathrm{y}\left(\mathrm{0}\right)=−\mathrm{1}\:,\mathrm{y}^{'} \left(\mathrm{0}\right)=\mathrm{0}\:,\mathrm{y}^{\left(\mathrm{2}\right)} \left(\mathrm{0}\right)\:=\mathrm{1} \\ $$ Answered by mathmax by abdo…
Question Number 30871 by ajfour last updated on 27/Feb/18 $${If}\:\:\:\mathrm{2}{f}\left({x}\right)+{f}\left(−{x}\right)=\frac{\mathrm{1}}{{x}}\mathrm{sin}\:\left({x}−\frac{\mathrm{1}}{{x}}\right) \\ $$$${Find}\:\:\:\int_{\mathrm{1}/{e}} ^{\:\:{e}} {f}\left({x}\right){dx}\:\:. \\ $$ Commented by abdo imad last updated on 27/Feb/18 $${let}\:{complete}\:{the}\:{work}\:{of}\:{sir}\:{mrw}_{\mathrm{2}}…
Question Number 96383 by bobhans last updated on 01/Jun/20 $$\mathrm{Find}\:\mathrm{domain}\:\&\:\mathrm{range}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{6}}\: \\ $$ Answered by john santu last updated on 01/Jun/20 $$\mathrm{The}\:\mathrm{domain}\:\mathrm{consists}\:\mathrm{of}\:\mathrm{all}\:\mathrm{real}\: \\…