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lim-n-1-n-1-n-

Question Number 74570 by Learner-123 last updated on 26/Nov/19 $${lim}_{{n}\rightarrow\infty} \frac{\mathrm{1}}{\left({n}\right)^{\frac{\mathrm{1}}{{n}}} }\:=\:? \\ $$ Answered by mind is power last updated on 26/Nov/19 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}n}^{−\frac{\mathrm{1}}{\mathrm{n}}}…

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…