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Category: Relation and Functions

let-f-x-n-1-x-n-2-with-x-1-1-prove-that-f-x-pi-2-ln-x-x-1-

Question Number 36751 by prof Abdo imad last updated on 05/Jun/18 $$\left.{let}\:\:{f}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{x}^{{n}^{\mathrm{2}} } \:\:\:{with}\:\:{x}\in\right]−\mathrm{1},\mathrm{1}\left[\right. \\ $$$${prove}\:{that}\:\:{f}\left({x}\right)\:\sim\:\frac{\sqrt{\pi}}{\mathrm{2}\sqrt{−{ln}\left({x}\right)}}\:\left({x}\:\rightarrow\mathrm{1}^{−} \right) \\ $$ Terms of Service Privacy…

let-f-t-n-1-1-n-ln-1-t-2-n-1-t-2-1-study-the-simple-and-uniform-convergence-of-f-n-2-study-the-continuity-of-f-3-prove-that-lim-t-f-t-ln-2-pi-

Question Number 36750 by prof Abdo imad last updated on 05/Jun/18 $${let}\:{f}\left({t}\right)=\sum_{{n}\geqslant\mathrm{1}} \:\left(−\mathrm{1}\right)^{{n}} {ln}\left\{\mathrm{1}+\:\frac{{t}^{\mathrm{2}} }{{n}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}\right\} \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{simple}\:\:{and}\:{uniform}\:{convergence} \\ $$$${of}\:\Sigma\:{f}_{{n}} \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{continuity}\:{of}\:{f} \\ $$$$\left.\mathrm{3}\right)\:{prove}\:{that}\:{lim}_{{t}\rightarrow+\infty} \:{f}\left({t}\right)={ln}\left(\frac{\mathrm{2}}{\pi}\right)\:.…

let-f-x-n-1-1-n-1-ln-nx-1-give-D-f-and-study-f-on-1-2-study-the-continjity-of-f-and-calculate-lim-x-1-f-x-and-lim-x-f-x-3-prove-that-f-is-C-1-on-1-

Question Number 36748 by prof Abdo imad last updated on 05/Jun/18 $${let}\:{f}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{ln}\left({nx}\right)} \\ $$$$\left.\mathrm{1}\left.\right)\:{give}\:{D}_{{f}} \:\:{and}\:{study}\:{f}\:{on}\right]\mathrm{1},+\infty\left[\right. \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{continjity}\:{of}\:{f}\:{and}\:{calculate} \\ $$$${lim}\:_{{x}\rightarrow\mathrm{1}} {f}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right). \\…

let-f-x-n-1-1-n-cos-n-x-sin-nx-1-prove-the-convergence-of-this-serie-2-prove-that-f-is-C-2-on-R-kpi-k-Z-and-calculate-f-x-3-give-a-exprrssion-of-f-

Question Number 36744 by prof Abdo imad last updated on 05/Jun/18 $${let}\:{f}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}}\:{cos}^{{n}} \left({x}\right){sin}\left({nx}\right) \\ $$$$\left.\mathrm{1}\right){prove}\:{the}\:{convergence}\:{of}\:{this}\:{serie} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:{f}\:{is}\:{C}^{\mathrm{2}} \:{on}\:{R}\:−\left\{{k}\pi,{k}\in{Z}\right\}{and} \\ $$$${calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{give}\:{a}\:{exprrssion}\:{of}\:{f}.…