Category: Algebra

Question Number 195809 by mr W last updated on 11/Aug/23 $$if{x}^5+x+1=0,find{x}^3-x^2=?$$ Commented by jabarsing last updated on 11/Aug/23 $${hello}\:{dear}\:{W}, \…

Question Number 195733 by York12 last updated on 09/Aug/23 $$provethat$$$$\underset{n=2}{\sum ^{\mathrm{\infty }}}\left[\frac{B_{\stackrel{\mathrm{\_}}{n}}}{(n-2)!}\right]=\frac{e(3-e)}{{(e-1)}^3}$$$$where{B}_{\stackrel{\mathrm{\_}}{n}}isthen-th{bernouli}^{\prime }snumber$$ Answered by…

Question Number 195689 by Shomurotovdiyorbek last updated on 07/Aug/23 $$\int_{\mathrm{1}} ^{\mathrm{3}} {f}\left({x}\right)^{\mathrm{3}} {f}'\left({x}\right){dx}=\int_{\mathrm{1}} ^{\mathrm{3}} \left({f}\left({x}\right)^{\mathrm{3}} \right){df}\left({x}\right)=\int_{\mathrm{1}} ^{\mathrm{3}} {t}^{\mathrm{3}} {dt}=\frac{{t}^{\mathrm{4}} }{\mathrm{4}}\int_{\mathrm{1}} ^{\mathrm{3}} =\frac{{f}\left({x}\right)^{\mathrm{4}} }{\mathrm{4}}\int_{\mathrm{1}} \mathrm{3} \…

Question Number 195647 by mathlove last updated on 06/Aug/23 $$f\left(x\right)=\frac{1276}{{(x-1)}^{ln\frac{2}{4589}}}$$$$domainf\left(x\right)=?$$ Answered by Tokugami last updated on 17/Sep/23 $$\frac{\mathrm{1276}}{\left({x}−\mathrm{1}\right)^{\mathrm{ln}\left(\mathrm{2}\right)−\mathrm{ln}\left(\mathrm{4589}\right)} }=\mathrm{1276}\left({x}−\mathrm{1}\right)^{\mathrm{ln}\left(\mathrm{4589}\right)−\mathrm{ln}\left(\mathrm{2}\right)} \…

Question Number 195653 by mustafazaheen last updated on 06/Aug/23 Answered by MM42 last updated on 06/Aug/23 $$e-1>1$$$$\Rightarrow {lim}_{x\to 0^{+}}{(e-1)}^{\frac{\sqrt{3}}{x}}=\mathrm{\infty }$$$$\Rightarrow{lim}_{{x}\rightarrow\:\mathrm{0}^{−} }…