Question Number 33649 by rahul 19 last updated on 21/Apr/18 $${Consider}\:{f}:{R}^{+} \rightarrow{R}\:{such}\:{that} \\ $$$${f}\left(\mathrm{3}\right)=\mathrm{1}\:{for}\:{a}\in{R}^{+} \:{and}\: \\ $$$${f}\left({x}\right).{f}\left({y}\right)\:+\:{f}\left(\frac{\mathrm{3}}{{x}}\right).{f}\left(\frac{\mathrm{3}}{{y}}\right)\:=\:\mathrm{2}{f}\left({xy}\right) \\ $$$$\forall\:{x},{y}\:\in\:{R}^{+} .\:{Then}\:{find}\:{f}\left({x}\right)\:? \\ $$ Commented by rahul…
Question Number 99159 by bemath last updated on 19/Jun/20 Commented by som(math1967) last updated on 19/Jun/20 $$\mathrm{let}\:\mathrm{pt}.\:\mathrm{on}\:\mathrm{paabola}\:\left(\mathrm{h},\mathrm{k}\right) \\ $$$$\therefore\sqrt{\left(\mathrm{h}+\mathrm{3}\right)^{\mathrm{2}} +\left(\mathrm{k}−\mathrm{3}\right)^{\mathrm{2}} }=\frac{\mid\mathrm{k}−\mathrm{7}\mid}{\:\sqrt{\mathrm{1}^{\mathrm{2}} }} \\ $$$$\Rightarrow\left(\mathrm{h}+\mathrm{3}\right)^{\mathrm{2}} +\left(\mathrm{k}−\mathrm{3}\right)^{\mathrm{2}}…
Question Number 33597 by abdo imad last updated on 19/Apr/18 $${study}\:{and}\:{give}\:{the}\:{graph}\:{of}\:{f}\left({x}\right)\:={e}^{\frac{\mathrm{2}}{{lnx}}} \:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33596 by abdo imad last updated on 19/Apr/18 $$\left.\mathrm{1}\right)\:{prove}\:{that}\:\forall\left({a},{b}\right)\in{R}^{\mathrm{2}} \:\:\:\:\mid{sinb}\:−{sina}\mid\leqslant\mid{b}−{a}\mid \\ $$$$\left.\mathrm{2}\right){let}\:{give}\:{the}\:{sequence}\:\:{x}_{\mathrm{0}} =\mathrm{0}\:{and} \\ $$$${x}_{{n}+\mathrm{1}} ={a}\:+\frac{\mathrm{1}}{\mathrm{2}}{sin}\left({x}_{{n}} \right)\:{prove}\:{that}\:{for}\:{m}\geqslant{n} \\ $$$$\mid{x}_{{m}} \:−{x}_{{n}} \mid\:\leqslant\:\:\frac{\mid{a}\mid}{\mathrm{2}^{{n}−\mathrm{1}} } \\…
Question Number 33591 by abdo imad last updated on 19/Apr/18 $${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\mathrm{2}}{{n}^{\mathrm{3}} \:\:+\mathrm{3}{n}^{\mathrm{2}} \:+\mathrm{2}{n}}\:. \\ $$ Commented by abdo imad last updated on 20/Apr/18…
Question Number 33592 by abdo imad last updated on 19/Apr/18 $${let}\:{f}\left({x}\right)\:={e}^{−{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{f}^{\left({n}\right)} \left({x}\right)\:=\:{p}_{{n}} \left({x}\right).{e}^{−{x}^{\mathrm{2}} } \:\:\:{where}\:{p}_{{n}} {is}\:{a}\:{polynome} \\ $$$${with}\:{deg}={n} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\forall\:{n}\geqslant\mathrm{1}\: \\ $$$${p}_{{n}+\mathrm{1}}…
Question Number 33588 by abdo imad last updated on 19/Apr/18 $${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}\:. \\ $$ Commented by abdo imad last updated on 20/Apr/18 $${let}\:{put}\:{S}_{{n}}…
Question Number 33586 by abdo imad last updated on 19/Apr/18 $${find}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{z}^{{n}} \:\:\frac{{sin}\left({n}\theta\right)}{{n}}\:\:{with}\:{z}\:{from}\:{C}\:{and}\:\mid{z}\mid<\mathrm{1}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33584 by abdo imad last updated on 19/Apr/18 $${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(\mathrm{1}+{i}\right)^{{n}} \:{cos}\left({n}\theta\right)}{\mathrm{2}^{{n}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33585 by abdo imad last updated on 19/Apr/18 $${study}\:{the}\:{nature}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} {sin}\left(\pi{en}!\right)\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com