Category: Relation and Functions

Question Number 82920 by abdomathmax last updated on 25/Feb/20 $$calculate{lim}_{x\to 0}\frac{ln(1+ln(1+x))}{x}$$ Answered by mind is power last updated on 25/Feb/20 $$ln(1+x)\sim x$$$$\Rightarrow{ln}\left(\mathrm{1}+{ln}\left(\mathrm{1}+{x}\right)\right)\sim{ln}\left(\mathrm{1}+{x}\right)…

Question Number 17354 by ajfour last updated on 04/Jul/17 $$\mathrm{Solve}\mathrm{for}\mathrm{x}:$$$$\mid \mathrm{x}-1\mid -\mid \mathrm{x}-2\mid +\mid \mathrm{x}+1\mid >\mid \mathrm{x}+2\mid +\mid \mathrm{x}\mid -3.$$ Commented by ajfour last updated on 04/Jul/17 $$\mathrm{my}\mathrm{answer}:\mathrm{x}\in (-3,3)-\{-1,1\}$$$$\mathrm{answer}\:\mathrm{in}\:\mathrm{book}:\:\:\mathrm{x}\in\:\left(\mathrm{1},\:\mathrm{3}\right)\:. \…

Question Number 148371 by mathmax by abdo last updated on 27/Jul/21 $$\mathrm{calculate}{\int }_{\gamma }{\mathrm{ze}}^{\frac{2}{{\mathrm{z}}^2}}\mathrm{dz}\mathrm{with}\gamma \left(\mathrm{t}\right)=\sqrt{3}{\mathrm{e}}^{\mathrm{it}}\mathrm{t}\in [0,2\pi ]$$ Answered by mathmax by abdo last updated…

Question Number 148302 by mathmax by abdo last updated on 26/Jul/21 $$\mathrm{calculate}{\int }_{\mid \mathrm{z}\mid =3}\frac{\cos \left(2\mathrm{iz}\right)}{(\mathrm{z}-2\mathrm{i}){(\mathrm{z}+\mathrm{i}\sqrt{3})}^2}\mathrm{dz}$$ 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 148237 by puissant last updated on 26/Jul/21 $$f\left(t\right)=sin\left(pt\right)fourierserie..$$ 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} \…