Category: Relation and Functions

Question Number 52669 by maxmathsup by imad last updated on 11/Jan/19 $$let{S}_n\left(p\right)=\sum _{k=0}^n{k}^p$$$${prove}\:{that}\:{S}_{{n}} \left({p}\right)=\frac{\mathrm{1}}{{p}+\mathrm{1}}\left\{\:\left({n}+\mathrm{1}\right)^{{p}+\mathrm{1}} \:−\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{C}_{{p}+\mathrm{1}} ^{{k}} \:{S}_{{n}} \left({k}\right)\right\} \…

Question Number 183712 by Michaelfaraday last updated on 29/Dec/22 $$solve:$$$$W\left(In\left(4x\right)\right)=\sqrt{(x-1)}$$ Answered by mr W last updated on 29/Dec/22 $${e}^{\mathrm{ln}\:\left(\mathrm{4}{x}\right)} \mathrm{ln}\:\left(\mathrm{4}{x}\right)=\sqrt{{x}−\mathrm{1}} \…

Question Number 117857 by bemath last updated on 14/Oct/20 $$\mathrm{Let}\mathrm{n}\in \mathbb{N}.\mathrm{Find}\mathrm{the}\mathrm{number}\mathrm{of}$$$$\mathrm{polynomials}\mathrm{p}\left(\mathrm{x}\right)\mathrm{with}\mathrm{coefficients}$$$$\mathrm{in}\{0,1,2,3\}\mathrm{such}\mathrm{that}\mathrm{p}\left(2\right)=\mathrm{n}$$ Answered by mindispower last updated on 14/Oct/20 $${let}\:{p}\left({x}\right)=\underset{{k}\leqslant{n}} {\sum}{a}_{{k}}…

Question Number 183158 by cortano1 last updated on 21/Dec/22 $$Givenf\left(x\right)=\frac{\left[\frac{1}{3}x\right]\mid 2x\mid +Ax}{\mid 4-x^2\mid }$$$$iff{}^{\prime }(-1)=5thenA=?$$$$\left[\right]=floorfunction$$ Answered by TheSupreme last updated on 21/Dec/22 $${f}\left({x}\right)=\frac{{g}\left({x}\right){h}\left({x}\right)}{{u}\left({x}\right)}+\frac{{Ax}}{\mathrm{4}−{x}^{\mathrm{2}}…

Question Number 51996 by maxmathsup by imad last updated on 01/Jan/19 $$calculate{S}_n=\sum _{k=0}^{n-1}sin(\frac{\pi }{4n}+\frac{k\pi }{2n})$$$$$$ Commented by Abdo msup. last updated…