Category: Relation and Functions

Question Number 23922 by chernoaguero@gmail.com last updated on 09/Nov/17 $$\mathbf{if}\mathbf{f}\left(\mathbf{x}\right)=2^{\mathbf{x}}$$$$\mathbf{show}\mathbf{that}\mathbf{f}(\mathbf{x}+3)-\mathbf{f}(\mathbf{x}-1)=\frac{15}{2}\mathbf{f}\left(\mathbf{x}\right)$$ Answered by $@ty@mlastupdatedon10/Nov/17$${f}\left({x}+\mathrm{3}\right)=\mathrm{2}^{{x}+\mathrm{3}} =\mathrm{2}^{{x}} .\mathrm{2}^{\mathrm{3}} =\mathrm{8}.\mathrm{2}^{{x}}…

Question Number 23785 by tawa tawa last updated on 06/Nov/17 $$\mathrm{A}\mathrm{function}\mathrm{f}\mathrm{is}\mathrm{define}\mathrm{by}\mathrm{f}:\to 3-2\mathrm{sinx},\mathrm{for}0⩽\mathrm{x}⩽360$$$$\mathrm{find}\mathrm{the}\mathrm{range}\mathrm{of}\mathrm{f}$$ Answered by mrW1 last updated on 06/Nov/17 $$\sin x\in [-1,+1]$$$${f}=\mathrm{3}−\mathrm{2sin}\:{x}\:\in\left[\mathrm{1},\mathrm{5}\right]…

Question Number 89313 by abdomathmax last updated on 16/Apr/20 $$findthesum\sum _{n=1}^{\mathrm{\infty }}\frac{1}{n^2\times 3^n}$$ Commented by mathmax by abdo last updated on 19/Apr/20…

Question Number 23518 by Tinkutara last updated on 01/Nov/17 $$\mathrm{A}\mathrm{ball}\mathrm{of}\mathrm{mass}1\mathrm{kg}\mathrm{moving}\mathrm{with}\mathrm{velocity}$$$$3\mathrm{m}/\mathrm{s}\mathrm{collides}\mathrm{with}\mathrm{spring}\mathrm{of}\mathrm{natural}$$$$\mathrm{length}2\mathrm{m}\mathrm{and}\mathrm{force}\mathrm{constant}144\mathrm{N}/\mathrm{m}.$$$$\mathrm{What}\mathrm{will}\mathrm{be}\mathrm{length}\mathrm{of}\mathrm{compressed}$$$$\mathrm{spring}?$$ Commented by Tinkutara last updated…

Question Number 154467 by talminator2856791 last updated on 18/Sep/21 $$$$$$\underset{n=1}{\prod ^{\mathrm{\infty }}}\frac{{(1+\frac{1}{n})}^{\frac{1}{2}}}{1+\frac{1}{2n}}$$$$$$ Answered by alisiao last updated on…