Question Number 94078 by Rio Michael last updated on 16/May/20 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{function}\:{f}\:\mathrm{defined}\:\mathrm{by}\:{f}\left({x}\right)\:=\:\frac{\mid{x}−\mathrm{2}\mid}{\mathrm{1}−\mid{x}\mid} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{state}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:{f}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\:\:\:\:\:{f}\left({x}\right)\:=\:\begin{cases}{\frac{\mathrm{2}−{x}}{\mathrm{1}+{x}}\:,\:{x}\:<\:\mathrm{0}}\\{\frac{\mathrm{2}−{x}}{\mathrm{1}−{x}},\:\mathrm{0}\:\leqslant\:{x}\:<\:\mathrm{2}}\\{\frac{{x}−\mathrm{2}}{\mathrm{1}−{x}}\:,\:{x}\:\geqslant\:\mathrm{2}}\end{cases} \\ $$$$\left(\mathrm{iii}\right)\:\mathrm{Investigate}\:\mathrm{the}\:\mathrm{continuity}\:\mathrm{of}\:{f}\:\mathrm{at}\:{x}\:=\:\mathrm{2}. \\ $$ Terms of Service Privacy…
Question Number 94079 by Rio Michael last updated on 16/May/20 $$\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\frac{\mathrm{3}{x}−\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{4}}\:{dx}\:=\:? \\ $$ Answered by Kunal12588 last updated on 16/May/20 $$\frac{\mathrm{3}}{\mathrm{2}}\left[\int_{\mathrm{2}} ^{\mathrm{4}}…
Question Number 159560 by LEKOUMA last updated on 18/Nov/21 $${Resolve}\: \\ $$$$\mathrm{1}.\:{u}_{{n}+\mathrm{2}} −\mathrm{2}{u}_{{n}+\mathrm{1}} +\mathrm{4}{u}_{{n}} =\mathrm{3}^{{n}} \\ $$$${with}\:{u}_{{o}} =\mathrm{1},\:{u}_{\mathrm{1}} =−\mathrm{2} \\ $$$$\mathrm{2}.\:{u}_{{n}} ={u}_{{n}−\mathrm{1}} −{u}_{{n}−\mathrm{2}} +\mathrm{2sin}\:\left(\frac{{n}\Pi}{\mathrm{3}}\right) \\…
Question Number 28481 by karteek1174 last updated on 26/Jan/18 Commented by mrW2 last updated on 26/Jan/18 $${please}\:{supply}\:{image}\:{with}\:{better}\:{quality}\:{sir}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 28431 by abdo imad last updated on 25/Jan/18 $${let}\:{give}\:{w}_{{k}} =\:{e}^{{i}\frac{\mathrm{2}{k}\pi}{{n}}} \:\:\:{k}\in{Z}\:\:\:{find}\:{the}\:{value}\:{of} \\ $$$$\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \left(\mathrm{1}+\frac{\mathrm{2}}{\mathrm{2}−{w}_{{k}} \:}\right). \\ $$ Terms of Service Privacy Policy…
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Question Number 159403 by LEKOUMA last updated on 16/Nov/21 $${U}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}\left({u}_{{n}} +\frac{{a}}{{u}_{{n}} }\right)\:{with}\:{u}_{\mathrm{1}} >\mathrm{0},\:\:{a}>\mathrm{0} \\ $$$${Prove}\:{that}\:\:\frac{{u}_{{n}+\mathrm{1}} }{{u}_{{n}} }\leqslant\mathrm{1} \\ $$ Commented by mathmax by abdo…
Question Number 93787 by Ar Brandon last updated on 14/May/20 Commented by mathmax by abdo last updated on 15/May/20 $$\frac{\mathrm{4}{k}}{\mathrm{4}{k}^{\mathrm{4}} \:+\mathrm{1}}\:=\frac{\mathrm{4}{k}}{\left(\sqrt{\mathrm{2}}{k}\right)^{\mathrm{4}} +\mathrm{1}}\:=\frac{\mathrm{4}{k}}{\left(\left(\sqrt{\mathrm{2}}{k}\right)^{\mathrm{2}} \right)^{\mathrm{2}} \:+\mathrm{1}}\:=\frac{\mathrm{4}{k}}{\left(\mathrm{2}{k}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}}…
Question Number 159309 by LEKOUMA last updated on 15/Nov/21 $${Resolve}\:{I}_{{n}} =\int_{−\mathrm{1}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{{n}} {dx} \\ $$ Answered by mathmax by abdo last updated on…