Category: Relation and Functions

Question Number 65739 by Masumsiddiqui399@gmail.com last updated on 03/Aug/19 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 65677 by mathmax by abdo last updated on 01/Aug/19 $$let{S}_n=\sum _{k=1}^n\frac{1}{\sqrt{k^2+k}}$$$$1)findaequivalentof{S}_{n}whenn\to +\mathrm{\infty }$$$$2)provethat\left(S_n\right)isconvergent.$$ Terms…

Question Number 65664 by mathmax by abdo last updated on 01/Aug/19 $$solve\frac{\sqrt{1-x}-\sqrt{2x+1}}{\sqrt{1-x}+\sqrt{2x+1}}=\frac{x+1}{3}$$ Answered by MJS last updated on 01/Aug/19 $$\frac{\sqrt{1-x}-\sqrt{2x+1}}{\sqrt{1-x}+\sqrt{2x+1}}=\frac{{(\sqrt{1-x}-\sqrt{2x+1})}^2}{(\sqrt{1-x}+\sqrt{2x+1})(\sqrt{1-x}-\sqrt{2x+1})}=$$$$=\frac{{x}+\mathrm{2}−\mathrm{2}\sqrt{\mathrm{1}−{x}}\sqrt{\mathrm{2}{x}+\mathrm{1}}}{−\mathrm{3}{x}}=−\frac{{x}+\mathrm{2}}{\mathrm{3}{x}}+\frac{\mathrm{2}\sqrt{\mathrm{1}−{x}}\sqrt{\mathrm{2}{x}+\mathrm{1}}}{\mathrm{3}{x}}…

Question Number 143987 by liberty last updated on 20/Jun/21 $$Iff(x^2-6x+6)+f(x^2-4x+4)=2x$$$$\mathrm{\forall }x\in Rth\mathrm{e}nf(-3)+f\left(9\right)-5f\left(1\right)=?$$ Answered by mitica last updated on 20/Jun/21 $${x}=\mathrm{1}\Rightarrow{f}\left(\mathrm{1}\right)+{f}\left(\mathrm{1}\right)=\mathrm{2}\Rightarrow{f}\left(\mathrm{1}\right)=\mathrm{1} \…

Question Number 143860 by mathmax by abdo last updated on 19/Jun/21 $$\mathrm{calculate}{\int }_0^{\mathrm{\infty }}\mathrm{x}{\mathrm{e}}^{-{\mathrm{x}}^2}\log (1+{\mathrm{e}}^{\mathrm{x}})\mathrm{dx}$$ Answered by mathmax by abdo last…