Category: Arithmetic

Question Number 77687 by jagoll last updated on 09/Jan/20 $$givenfunction$$$$f\left(x\right)=f(x+2)for\mathrm{\forall }x\in \mathbb{R}$$$$if\underset{0}{\stackrel{2}{\int }}f\left(x\right)dx=B,whatvalueof$$$$\underset{3}{\stackrel{7}{\int }}f(x+8)dx=?$$ Commented by mr…

Question Number 143134 by help last updated on 10/Jun/21 Answered by liberty last updated on 10/Jun/21 $$y^{\prime }=\underset{h\to 0}{\lim }\frac{\cos ({(x+h)}^2-4(x+h))-\cos (x^2-4x)}{h}$$$$=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\left({x}^{\mathrm{2}} +\mathrm{2}{hx}+{h}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{4}{h}\right)−\mathrm{cos}\:\left({x}^{\mathrm{2}}…

Question Number 11994 by algabara last updated on 09/Apr/17 $$4x=60$$ Commented by tawa last updated on 09/Apr/17 $$4\mathrm{x}=60$$$$\mathrm{Divide}\mathrm{both}\mathrm{side}\mathrm{by}4$$$$\frac{\mathrm{4x}}{\mathrm{4}}\:=\:\frac{\mathrm{60}}{\mathrm{4}} \…

Question Number 11823 by Joel576 last updated on 01/Apr/17 $$3+2\left(3^2\right)+3\left(3^3\right)+\dots +10\left(3^{10}\right)=?$$ Answered by ajfour last updated on 02/Apr/17 $${S}=\:\mathrm{3}+\mathrm{2}\left(\mathrm{3}\right)^{\mathrm{2}} +\mathrm{3}\left(\mathrm{3}\right)^{\mathrm{3}} +…+\mathrm{10}\left(\mathrm{3}\right)^{\mathrm{10}}…

Question Number 77285 by jagoll last updated on 05/Jan/20 $$\mathrm{how}\mathrm{to}\mathrm{find}\mathrm{the}$$$$\mathrm{Fourier}\mathrm{series}\mathrm{of}\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x},0<\mathrm{x}<\frac{1}{8}$$ Answered by john santu last updated on 05/Jan/20 $$\mathrm{because}\mathrm{f}\left(\mathrm{x}\right)\mathrm{an}\mathrm{odd}\mathrm{function}$$$$,\:\mathrm{we}\:\mathrm{used}\:\mathrm{the}\:\mathrm{sine}\:\mathrm{series}.…