Question Number 138860 by qaz last updated on 19/Apr/21 $${Prove}::\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{3}} −\mathrm{sin}\:^{\mathrm{3}} {x}}{{x}^{\mathrm{5}} }{dx}=\frac{\mathrm{13}}{\mathrm{32}}\pi \\ $$ Answered by Dwaipayan Shikari last updated on 19/Apr/21…
Question Number 73327 by mathmax by abdo last updated on 10/Nov/19 $${let}\:{w}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{lnt}}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{explicit}\:{w}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{lnt}}{\left({n}^{\mathrm{2}} \:+{t}^{\mathrm{2}}…
Question Number 138863 by bramlexs22 last updated on 19/Apr/21 $$\mid\mathrm{2x}−\mathrm{1}\mid\:\leqslant\:\frac{\mathrm{4}}{\:\sqrt{\mathrm{x}+\mathrm{2}}}\:+\:\mathrm{1} \\ $$ Answered by lyubita last updated on 19/Apr/21 $$-\:\mathrm{2}\:<\:{x}\:\leqslant\:\mathrm{2} \\ $$ Commented by bramlexs22…
Question Number 7788 by Chantria last updated on 15/Sep/16 $$\left({a}_{{n}} \right)_{{n}\in{N}} \:{such}\:{that}\:{a}_{\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}\: \\ $$$${and}\:{a}_{{n}+\mathrm{1}} =\frac{{a}_{{n}} ^{\mathrm{2}} }{{a}_{{n}} ^{\mathrm{2}} −{a}_{{n}} +\mathrm{1}} \\ $$$${Prove}\:{that}\:{a}_{\mathrm{1}} +{a}_{\mathrm{2}} +{a}_{\mathrm{3}}…
Question Number 7785 by B last updated on 15/Sep/16 $${x}^{\mathrm{2}} −{x}^{\mathrm{2}} ={x}^{\mathrm{2}} −{x}^{\mathrm{2}} \\ $$$$\left({x}−{x}\right)\left({x}+{x}\right)={x}\left({x}−{x}\right) \\ $$$${x}−{x}={x} \\ $$$$\mathrm{2}{x}={x} \\ $$$$\mathrm{2}=\mathrm{1} \\ $$ Commented by…
Question Number 7782 by Chantria last updated on 15/Sep/16 $$\:{Given}\:{a},{b},{c}\:\in{N}\:;\:{prove}\:{that} \\ $$$$\:\frac{\mathrm{1}+{a}}{\mathrm{1}+\mathrm{2}{a}}\:+\:\frac{\mathrm{1}+{b}}{\mathrm{1}+\mathrm{2}{b}}\:+\:\frac{\mathrm{1}+{c}}{\mathrm{1}+\mathrm{2}{c}}\:\leqslant\:\mathrm{2} \\ $$ Commented by sou1618 last updated on 15/Sep/16 $${Let}\:{f}\left({n}\right)=\frac{\mathrm{1}+{n}}{\mathrm{1}+\mathrm{2}{n}}\:\:\left({n}\geqslant\mathrm{1}\right) \\ $$$$ \\…
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Question Number 7781 by 314159 last updated on 15/Sep/16 Commented by prakash jain last updated on 15/Sep/16 $${f}\left(\mathrm{1}\right)=\mathrm{2} \\ $$$${f}\left(\mathrm{2}\right)=\mathrm{8} \\ $$$${f}\left({x}+{y}\right)−{kxy}={f}\left({x}\right)+\mathrm{2}{y}^{\mathrm{2}} \\ $$$${x}=\mathrm{0} \\…
Question Number 138851 by bramlexs22 last updated on 19/Apr/21 $${Find}\:{max}\:{value}\:{of}\: \\ $$$${x}^{\mathrm{2}} −\mathrm{3}{xy}−\mathrm{2}{y}^{\mathrm{2}} \:{subject}\:{to}\: \\ $$$${x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} =\mathrm{1}. \\ $$ Answered by ajfour last updated…
Question Number 138850 by bramlexs22 last updated on 19/Apr/21 $${x}^{−\mathrm{log}\:\left({x}\right)+\mathrm{4}} \:<\:\frac{\mathrm{1}}{\mathrm{16}}{x}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com