Category: Others

Question Number 69715 by Mikaell last updated on 26/Sep/19 $$\int\frac{{x}^{\mathrm{2}} +\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{e}^{{x}} {dx} \\ $$ Answered by mind is power last updated on 27/Sep/19 $$\int\frac{{x}^{\mathrm{2}}…

Question Number 4158 by 123456 last updated on 30/Dec/15 $$\mathrm{if} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{f}\left({x}\right)}{{g}\left({x}\right)}=\mathrm{1} \\ $$$$\mathrm{does} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}{f}\left({x}\right)−{g}\left({x}\right)=\mathrm{0}? \\ $$ Commented by 123456 last updated…

Question Number 4100 by 123456 last updated on 28/Dec/15 $$\mathrm{lets}\:{f}\:\mathrm{continuous}\:\mathrm{and}\:\mathrm{diferrenciable} \\ $$$${f}\left({x}+\mathrm{1}\right)={xf}\left({x}\right) \\ $$$$\mathrm{proof}\:\mathrm{that}\:{n}\in\mathbb{N}/\left\{\mathrm{0}\right\} \\ $$$${f}^{\left({n}\right)} \left({x}+\mathrm{1}\right)={nf}^{\left({n}−\mathrm{1}\right)} \left({x}\right)+{xf}^{\left({n}\right)} \left({x}\right) \\ $$$$\mathrm{where} \\ $$$${f}^{\left({n}\right)} \left({x}\right)=\frac{{d}^{{n}} {f}}{{dx}^{{n}}…

Question Number 135169 by bramlexs22 last updated on 11/Mar/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\: \\ $$$$\mathrm{x}^{\mathrm{81}} +\mathrm{x}^{\mathrm{49}} +\mathrm{x}^{\mathrm{25}} +\:\mathrm{x}^{\mathrm{9}} +\:\mathrm{x}\:\mathrm{is}\:\mathrm{divided} \\ $$$$\mathrm{by}\:\mathrm{x}^{\mathrm{3}} +\mathrm{x}\: \\ $$ Terms of Service Privacy…

Question Number 4025 by 123456 last updated on 26/Dec/15 $${f}_{{n}+\mathrm{1}} \left({x}\right)={x}^{{f}_{{n}} \left({x}\right)} \\ $$$${g}_{{n}+\mathrm{1}} \left({x}\right)=\left[{g}_{{n}} \left({x}\right)\right]^{{x}} \\ $$$${h}_{{n}+\mathrm{1}} \left({x}\right)=\left[{h}_{{n}} \left({x}\right)\right]^{{h}_{{n}} \left({x}\right)} \\ $$$${f}_{\mathrm{0}} \left({x}\right)={g}_{\mathrm{0}} \left({x}\right)={h}_{\mathrm{0}}…