Category: Algebra

Question Number 151767 by mathdanisur last updated on 22/Aug/21 $$\underset{\mathbf{n}\to \mathrm{\infty }}{\lim }\underset{\mathbf{k}=1}{\sum ^{\mathrm{\infty }}}\frac{\mathrm{n}}{{\mathrm{n}}^2+\mathrm{k}}=?$$ Answered by Olaf_Thorendsen last updated on 22/Aug/21 $$\mathrm{my}\:\mathrm{calculous}\:\mathrm{was}\:\mathrm{false}. \…

Question Number 151758 by mathdanisur last updated on 22/Aug/21 $$\mathrm{f}(3\mathrm{x}+1)={\mathrm{g}}^{-1}({5\mathrm{x}}^2-2)$$$${\left(gof\right)}^{{}^{\prime }}\left(4\right)=?$$ Commented by otchereabdullai@gmail.com last updated on 23/Aug/21 $$\mathrm{nice}!…

Question Number 20671 by Tinkutara last updated on 31/Aug/17 $$Thetotalnumberofpositiveintegral$$$$solution\left(s\right)oftheinequation$$$$\frac{x^2{(3x-4)}^3{(x-2)}^4}{{(x-5)}^5{(2x-7)}^6}⩽0is/are$$ Answered by ajfour last…

Question Number 151747 by mathdanisur last updated on 22/Aug/21 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)=\frac{\lambda -\mathrm{x}}{1+{\mathrm{x}}^2}\mathrm{and}\lambda ⩾\frac{-3}{4}$$$$\mathrm{solve}\mathrm{in}\mathbb{R}\mathrm{f}\left(\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\right)⩽0$$ Answered by mr W last updated on 22/Aug/21 $${say}\:{g}\left({x}\right)={f}\left({f}\left({x}\right)\right) \…

Question Number 20652 by Tinkutara last updated on 30/Aug/17 $$\mathrm{Suppose}x\mathrm{is}\mathrm{a}\mathrm{positive}\mathrm{real}\mathrm{number}$$$$\mathrm{such}\mathrm{that}\left\{x\right\},\left[x\right]\mathrm{and}x\mathrm{are}\mathrm{in}\mathrm{a}$$$$\mathrm{geometric}\mathrm{progression}.\mathrm{Find}\mathrm{the}\mathrm{least}$$$$\mathrm{positive}\mathrm{integer}n\mathrm{such}\mathrm{that}{x}^n>100.$$$$(\mathrm{Here}\left[x\right]\mathrm{denotes}\mathrm{the}\mathrm{integer}\mathrm{part}\mathrm{of}x$$$$\mathrm{and}\left\{x\right\}=x-\left[x\right].)$$ Commented by…