Category: Relation and Functions

Question Number 33847 by prof Abdo imad last updated on 26/Apr/18 $$letgiveasequenceofrealnumbetspositif$$$${\left(a_i\right)}_{1⩽i⩽n}$$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\left(\sum_{{i}=\mathrm{1}} ^{{n}} \:{a}_{{i}} \right)^{\mathrm{2}} \leqslant\:{n}\:\sum_{{i}=\mathrm{1}} ^{{n}} \:{a}_{{i}} ^{\mathrm{2}} \…

Question Number 33818 by rahul 19 last updated on 25/Apr/18 $$\mathit{L}etf:\mathit{R}\to [1,\mathrm{\infty })bedefinedas$$$$f\left(x\right)={\log }_{10}(\sqrt{3x^2-4x+\mathit{k}+1}+10).$$$$\mathit{I}ff\left(x\right)is\mathit{s}\mathit{u}\mathit{r}\mathit{j}\mathit{e}\mathit{c}\mathit{t}\mathit{i}\mathit{v}\mathit{e},thenfind$$$$thevalueof\mathit{k}?$$ Answered by MJS last…

Question Number 164874 by cortano1 last updated on 22/Jan/22 Answered by mahdipoor last updated on 22/Jan/22 $$getx+\sqrt{x^2+1}=t\Rightarrow x^2+1=t^2+x^2-2xt$$$$\Rightarrow\:\frac{{t}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}{t}}={x} \…

Question Number 33719 by prof Abdo imad last updated on 22/Apr/18 $$simplify{S}_n\left(x\right)=(1+x^2)(1+x^4)\dots .(1+x^{2^n})$$$$2)find{lim}_{n\to +\mathrm{\infty }}{S}_n\left(x\right)if\mid x\mid <1.$$ Commented by…

Question Number 33718 by prof Abdo imad last updated on 22/Apr/18 $$find\sum _{n=1}^{+\mathrm{\infty }}arctan\left(\frac{ln(1+\frac{1}{n+1})-ln(1+\frac{1}{n})}{1+(1+\frac{1}{n})(1+\frac{1}{n+1)}}\right)$$ Commented by prof Abdo imad last updated on 26/Apr/18…