Category: Relation and Functions

Question Number 143259 by Mathspace last updated on 12/Jun/21 $$solve{y}^{{}^{″}}-y^{{}^{\prime }}+2=xsin\left(3x\right)$$ Answered by qaz last updated on 12/Jun/21 $$\mathrm{y}_{\mathrm{p}} =\frac{\mathrm{1}}{\mathrm{D}^{\mathrm{2}} −\mathrm{D}}\left[\mathrm{xsin}\:\left(\mathrm{3x}\right)−\mathrm{2}\right] \…

Question Number 143255 by Mathspace last updated on 12/Jun/21 $$find{lim}_{x\to 0}\frac{sin(1-cosx)+1-cos\left(sinx\right)}{x^2}$$ Answered by bramlexs22 last updated on 12/Jun/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{sin}\:\left(\mathrm{1}−\mathrm{cos}\:{x}\right)}{\mathrm{1}−\mathrm{cos}\:{x}}.\left(\mathrm{1}−\mathrm{cos}\:{x}\right)+\mathrm{1}−\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)}{{x}^{\mathrm{2}} } \…

Question Number 143254 by Mathspace last updated on 12/Jun/21 $$findthevalueof\sum _{n=1}^{\mathrm{\infty }}\frac{{(-1)}^n}{n^2(n+1)(n+2)(n+3)}$$ Answered by Olaf_Thorendsen last updated on 12/Jun/21 $${R}\left({n}\right)\:=\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)}…

Question Number 77616 by BK last updated on 08/Jan/20 Commented by MJS last updated on 08/Jan/20 $$\mathrm{are}\mathrm{you}\mathrm{serious}\mathrm{on}\mathrm{this}\mathrm{one}?$$$$\mathrm{serious}\left(\begin{array}{c}BK\\ \mathrm{qu}.77616\end{array}\right)=\mathrm{true}\Rightarrow BK\ne \mathrm{serious}\mathrm{\forall }\mathrm{qu}.\in {\mathbb{N}}^{★}$$ Commented by BK last…

Question Number 143147 by mathmax by abdo last updated on 10/Jun/21 $$\mathrm{montrer}\mathrm{que}\mathrm{lasuite}{\mathrm{U}}_{\mathrm{n}}=\frac{{\mathrm{H}}_{\mathrm{n}}}{{\mathrm{n}}^2}\mathrm{est}\mathrm{bornee}$$$${\mathrm{H}}_{\mathrm{n}}=\sum _{\mathrm{k}=1}^{\mathrm{n}}\frac{1}{{\mathrm{n}}^2}$$ Commented by…