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prove-that-1-2-tan-1-x-cos-1-1-1-x-2-2-1-x-2-using-substitution-x-cos-2-

Question Number 74526 by Kunal12588 last updated on 25/Nov/19 $${prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{tan}^{−\mathrm{1}} {x}={cos}^{−\mathrm{1}} \left(\sqrt{\frac{\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{\mathrm{2}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}}\right) \\ $$$${using}\:{substitution}\:{x}={cos}\:\mathrm{2}\theta \\ $$ Answered by mind is power…

let-f-x-e-nx-ln-1-x-2-1-determine-f-n-x-and-f-n-0-2-developp-f-at-integr-serie-n-integr-natural-

Question Number 74502 by mathmax by abdo last updated on 25/Nov/19 $${let}\:{f}\left({x}\right)={e}^{−{nx}} {ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right){determine}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie}\:\:\:\left({n}\:{integr}\:{natural}\right) \\ $$ Commented by mathmax…

Question-74473

Question Number 74473 by arkanmath7@gmail.com last updated on 24/Nov/19 Commented by mathmax by abdo last updated on 24/Nov/19 $$\mid{z}−\mathrm{1}\mid=\mathrm{1}\:\Rightarrow{z}−\mathrm{1}={e}^{{i}\theta} \:\:\:\:\mathrm{0}\leqslant\theta\leqslant\pi\:\Rightarrow{z}=\mathrm{1}+{e}^{{i}\theta} \\ $$$$\int_{{C}} \left(\overset{−} {{z}}\right)^{\mathrm{2}} {dz}\:=\int_{\mathrm{0}}…