Category: Relation and Functions

Question Number 49639 by maxmathsup by imad last updated on 08/Dec/18 $$findarelationbetwen{\left[x\right]}^{2}and{[-x]}^2$$ Commented by Abdo msup. last updated on 23/Dec/18 $${if}\:{x}\in{Z}\:\:\:\left[{x}\right]^{\mathrm{2}} ={x}^{\mathrm{2}}…

Question Number 114878 by bobhans last updated on 21/Sep/20 $$Givenf\left(x\right)=\underset{0}{\stackrel{x}{\int }}\frac{dt}{\sqrt{1+t^3}}andg\left(x\right)bethe$$$$inversefunctionoff\left(x\right),theng{}^{″}\left(x\right)=\lambda g^2\left(x\right).$$$$thenthevalueof\lambda =$$ Answered by Olaf last updated…

Question Number 114597 by O Predador last updated on 19/Sep/20 $$$$$$\mathbf{What}\mathbf{is}\mathbf{the}\mathbf{number}\mathbf{value}\mathbf{of}\mathbf{f}\left[\sqrt[3]{\mathbf{log}\left(\frac{\sqrt{\mathbf{x}}-1}{\mathbf{x}-1}\right)}\right]=\sqrt{\sqrt{\mathbf{x}}+\mathbf{x}}\mathbf{for}\mathbf{f}(-1)?$$$$$$$$\mathbf{a})0,1$$$$\mathbf{b})27$$$$\mathbf{c})81$$$$\mathbf{d})10$$$$\left.\:\:\:\boldsymbol{\mathrm{e}}\right)\:\mathrm{12}…

Question Number 48506 by Abdo msup. last updated on 24/Nov/18 $$let{S}_n=\sum _{k=0}^{\mathrm{\infty }}\frac{{(-1)}^k}{2k+1}$$$$1)provethat\frac{\pi }{4}-S_n={(-1)}^{n+1}{\int }_0^1\frac{t^{2n+2}}{1+t^2}dt$$$$\left.\mathrm{2}\right)\:{conclude}\:{lim}_{{n}\rightarrow+\infty}…

Question Number 113904 by bobhans last updated on 16/Sep/20 $$If\{\begin{array}{l}f\left(x\right)=\sqrt{2x-5}\\ g\left(x\right)=x^2+1\end{array}$$$$find{(f^{-1}\circ g)}^{-1}\left(x\right)$$ Answered by bemath last updated on 16/Sep/20 $${solution}\::\:…