Question Number 89717 by abdomathmax last updated on 18/Apr/20 $${let}\:\:{f}\left({x}\right)=\mathrm{2}{x}−\sqrt{{x}−\mathrm{1}} \\ $$$${find}\:\int\:\:\:\frac{{f}^{−\mathrm{1}} \left({x}\right)}{{f}\left({x}\right)}{dx}\:\: \\ $$ Answered by MJS last updated on 19/Apr/20 $${y}=\mathrm{2}{x}−\sqrt{{x}−\mathrm{1}} \\ $$$$\mathrm{defined}\:\mathrm{for}\:{x}\geqslant\mathrm{1}…
Question Number 23922 by chernoaguero@gmail.com last updated on 09/Nov/17 $$\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{2}^{\boldsymbol{\mathrm{x}}} \\ $$$$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}+\mathrm{3}\right)−\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}−\mathrm{1}\right)=\frac{\mathrm{15}}{\mathrm{2}}\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right) \\ $$ Answered by $@ty@m last updated on 10/Nov/17 $${f}\left({x}+\mathrm{3}\right)=\mathrm{2}^{{x}+\mathrm{3}} =\mathrm{2}^{{x}} .\mathrm{2}^{\mathrm{3}} =\mathrm{8}.\mathrm{2}^{{x}}…
Question Number 23833 by Joel577 last updated on 07/Nov/17 $${f}\left({x}^{\mathrm{2}} \:+\:{x}\right)\:+\:\mathrm{2}{f}\left({x}^{\mathrm{2}} \:−\:\mathrm{3}{x}\:+\:\mathrm{2}\right)\:=\:\mathrm{9}{x}^{\mathrm{2}} \:−\:\mathrm{15}{x} \\ $$$$\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{f}\left(\mathrm{10}\right)\:? \\ $$ Commented by prakash jain last updated on 07/Nov/17…
Question Number 23785 by tawa tawa last updated on 06/Nov/17 $$\mathrm{A}\:\mathrm{function}\:\mathrm{f}\:\mathrm{is}\:\mathrm{define}\:\mathrm{by}\:\:\mathrm{f}\::\:\rightarrow\:\mathrm{3}\:−\:\mathrm{2sinx},\:\:\mathrm{for}\:\:\mathrm{0}\:\leqslant\:\mathrm{x}\:\leqslant\:\mathrm{360} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\:\mathrm{f} \\ $$ Answered by mrW1 last updated on 06/Nov/17 $$\mathrm{sin}\:{x}\in\left[−\mathrm{1},+\mathrm{1}\right] \\ $$$${f}=\mathrm{3}−\mathrm{2sin}\:{x}\:\in\left[\mathrm{1},\mathrm{5}\right]…
Question Number 89316 by abdomathmax last updated on 16/Apr/20 $${calculate}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\:\frac{\mathrm{2}{n}+\mathrm{1}}{\left({n}−\mathrm{1}\right)^{\mathrm{3}} \left({n}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 89313 by abdomathmax last updated on 16/Apr/20 $${find}\:{the}\:{sum}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} ×\mathrm{3}^{{n}} } \\ $$ Commented by mathmax by abdo last updated on 19/Apr/20…
Question Number 154668 by EDWIN88 last updated on 20/Sep/21 $$\:{If}\:{f}\left({x}\right)={f}\left({x}−\mathrm{1}\right)+{f}\left({x}+\mathrm{1}\right)\:{where} \\ $$$${f}\left(\mathrm{10}\right)=\mathrm{6}\:{and}\:{f}\left(\mathrm{20}\right)=\mathrm{2}{f}\left(\mathrm{21}\right) \\ $$$${then}\:{f}\left(\mathrm{16}\right)=\ldots? \\ $$ Commented by mathdanisur last updated on 20/Sep/21 $$\mathrm{f}\left(\mathrm{16}\right)\:=\:-\:\mathrm{f}\left(\mathrm{21}\right) \\…
Question Number 23518 by Tinkutara last updated on 01/Nov/17 $$\mathrm{A}\:\mathrm{ball}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{1}\:\mathrm{kg}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{velocity} \\ $$$$\mathrm{3}\:\mathrm{m}/\mathrm{s}\:\mathrm{collides}\:\mathrm{with}\:\mathrm{spring}\:\mathrm{of}\:\mathrm{natural} \\ $$$$\mathrm{length}\:\mathrm{2}\:\mathrm{m}\:\mathrm{and}\:\mathrm{force}\:\mathrm{constant}\:\mathrm{144}\:\mathrm{N}/\mathrm{m}. \\ $$$$\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{length}\:\mathrm{of}\:\mathrm{compressed} \\ $$$$\mathrm{spring}? \\ $$ Commented by Tinkutara last updated…
Question Number 154553 by talminator2856791 last updated on 19/Sep/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\:\Gamma\left({n}+\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)\:}{\:\Gamma\left({n}+\:\frac{\mathrm{1}}{{n}}\right)\:} \\ $$$$\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 154467 by talminator2856791 last updated on 18/Sep/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\left(\mathrm{1}+\:\frac{\mathrm{1}}{{n}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} }{\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{2}{n}}} \\ $$$$\: \\ $$ Answered by alisiao last updated on…