Category: Relation and Functions

Question Number 140071 by EDWIN88 last updated on 04/May/21 $$\mathrm{For}\mathrm{what}\mathrm{value}\mathrm{of}\mathrm{k}\mathrm{is}\mathrm{the}\mathrm{following}$$$$\mathrm{continous}\mathrm{function}?$$$$\mathrm{f}\left(\mathrm{x}\right)=\{\begin{array}{l}\frac{\sqrt{7\mathrm{x}+2}-\sqrt{6\mathrm{x}+4}}{\mathrm{x}-2};\mathrm{if}\mathrm{x}⩾-\frac{2}{7}\mathrm{\&}\mathrm{x}\ne 2\\ \mathrm{k};\mathrm{if}\mathrm{x}=2\end{array}$$ Answered by bobhans last updated on 04/May/21 $$\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right)=\underset{{x}\rightarrow\mathrm{2}}…

Question Number 74498 by mathmax by abdo last updated on 25/Nov/19 $$1)calculte{A}_n={\int }_0^{\mathrm{\infty }}{e}^{-nx}\left[e^x\right]dxwithnintegrandn⩾2$$$$2)find{lim}_{n\to +\mathrm{\infty }}{n}^n{A}_n$$ Commented by…

Question Number 139954 by Ar Brandon last updated on 02/May/21 Answered by mr W last updated on 03/May/21 $$x_{n+1}=\frac{x_n-\frac{1}{\sqrt{2}+1}}{1+x_n\times \frac{1}{\sqrt{2}+1}}$$$${let}\:\mathrm{tan}\:{A}_{{n}} ={x}_{{n}}…

Question Number 74352 by mathmax by abdo last updated on 22/Nov/19 $$let{U}_n=\sum _{k=0}^n\frac{1}{k^2+k+1}findaequivalentof{U}_n(n\to +\mathrm{\infty })$$$$$$ Answered by mind is…

Question Number 74351 by mathmax by abdo last updated on 22/Nov/19 $$findthevalueof\sum _{n=1}^{+\mathrm{\infty }}\frac{{(-1)}^n}{{(4n^2-1)}^2}$$ Commented by ~blr237~ last updated on…