Category: Algebra

Question Number 16374 by gourav~ last updated on 21/Jun/17 $$TheValueofthesum..\underset{n=1}{\sum ^{13}}(i^n+i^{n+1}),Wherei=\sqrt{-1}$$$$is..$$$$(a.)i$$$$(b.)i-1$$$$(c.)-i$$$$\left({d}.\right)\:\mathrm{0} \…

Question Number 147432 by mathdanisur last updated on 20/Jul/21 $$if\{\begin{array}{l}2x+a;x<-3\\ x^2-4;-3⩽x<2\\ x^2+ax+b;x⩾2\end{array}$$$$find3a-b=?$$ Answered by liberty last updated on 21/Jul/21 $$\left(\bullet\right)\:\underset{{x}\rightarrow−\mathrm{3}} {\mathrm{lim}}\:{f}\left({x}\right)=\underset{{x}\rightarrow−\mathrm{3}}…

Question Number 81892 by Power last updated on 16/Feb/20 Answered by MJS last updated on 16/Feb/20 $$\mathrm{we}\mathrm{can}\mathrm{find}\mathrm{a}\mathrm{formula}\mathrm{for}\mathrm{any}\mathrm{value}\mathrm{of}\mathrm{the}$$$$\mathrm{next}\mathrm{number}\Rightarrow \mathrm{the}\mathrm{answer}\mathrm{is}\mathrm{not}\mathrm{unique}$$ Commented by mr W…

Question Number 147402 by vvvv last updated on 20/Jul/21 $$\mathit{f}(\mathit{x}+1)(\mathit{x}+2)\dots .(\mathit{x}+2018)$$$${\mathit{f}}^{\prime }\left(0\right)=?$$ Answered by SEKRET last updated on 21/Jul/21 $$\mathbf{y}=(\mathbf{x}+1)(\mathbf{x}+2)\cdot \dots .(\mathbf{x}+2018)$$$$\:\:\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{y}}\right)\:=\:\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)+\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}+\mathrm{2}\right)+..+\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}+\mathrm{2018}\right) \…

Question Number 147371 by mathdanisur last updated on 20/Jul/21 $$ifx>0then:$$$$e^{\mathit{x}+{\mathit{e}}^{-\mathit{x}}}+e^{-\mathit{x}+{\mathit{e}}^{\mathit{x}}}⩾2coshx\cdot e^{\mathit{s}\mathit{e}\mathit{c}\mathit{h}\mathit{x}}$$ Answered by mindispower last updated on 20/Jul/21…