Question Number 66462 by mathmax by abdo last updated on 15/Aug/19 $$\left.\mathrm{1}\right){simplify}\:{S}_{{n}} \left({x}\right)=\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{cos}^{{k}} \left({x}\right){cos}\left({kx}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{cos}^{{k}}…
Question Number 926 by 123456 last updated on 26/Apr/15 $${a}\left({n},{m}\right)=\begin{cases}{{m}}&{{n}\leqslant\mathrm{0}}\\{{na}\left({n}+{m}−\mathrm{1},{m}\right)+{m}}&{{n}>\mathrm{0}\vee{m}\leqslant\mathrm{0}}\\{{na}\left({n}−{m},{m}−\mathrm{1}\right)+{m}+{m}^{\mathrm{2}} }&{{n}>\mathrm{0}\vee{m}>\mathrm{0}}\end{cases} \\ $$$${a}\left(\mathrm{5},\mathrm{5}\right)=??? \\ $$$${a}\left(\mathrm{10},\mathrm{10}\right)=?? \\ $$ Commented by 123456 last updated on 27/Apr/15 $${a}\left(\mathrm{0},{m}\right)={m}…
Question Number 66461 by adeee last updated on 15/Aug/19 $${x}\left({n}\right)=\mathrm{3}{n}^{\mathrm{2}} −\mathrm{2}{n}+\mathrm{7} \\ $$$${find}\:{even}\:{and}\:{odd}\:{component} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 923 by 123456 last updated on 25/Apr/15 $${f}\left({x},{y},{z}\right)={x}+{y}+{z} \\ $$$$\boldsymbol{{g}}\left({x},{y},{z}\right)=\left({x},{y},{z}\right) \\ $$$$\boldsymbol{{h}}\left({x},{y},{z}\right)=\boldsymbol{{g}}\left({x},{y},{z}\right)−\bigtriangledown{f}\left({x},{y},{z}\right)=??? \\ $$$$\bigtriangledown\centerdot\boldsymbol{{h}}\left({x},{y},{z}\right)=? \\ $$$$\bigtriangledown×\boldsymbol{{h}}\left({x},{y},{z}\right)=??? \\ $$ Answered by 2closedStringsMeet last updated…
Question Number 66459 by mathmax by abdo last updated on 15/Aug/19 $$\left.\mathrm{1}\right)\:{calculate}\:{by}\:{residus}\:{method}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} } \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{1}+{x}^{\mathrm{4}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} }{dx} \\ $$…
Question Number 922 by 123456 last updated on 25/Apr/15 $$\mathrm{find}\:\mathrm{the}\:\mathrm{fourier}\:\mathrm{serie}\:\mathrm{of} \\ $$$${f}\left({t}\right)=\mathrm{sinh}\left({t}\right) \\ $$$$\mathrm{into}\:\mathrm{the}\:\mathrm{interval}\:\left(−\mathrm{1},+\mathrm{1}\right) \\ $$ Answered by prakash jain last updated on 25/Apr/15 $${F}\left({w}\right)=\underset{{k}=−\infty}…
Question Number 921 by 112358 last updated on 24/Apr/15 $${How}\:{many}\:{arrays}\:{of}\:{the}\:{letters} \\ $$$${of}\:{the}\:{word}\:{BELMOPAN}\:{are}\: \\ $$$${possible}\:{if}\:{no}\:{two}\:{vowels}\:{come} \\ $$$${together}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131994 by liberty last updated on 10/Feb/21 Commented by liberty last updated on 10/Feb/21 $$\mathrm{old}\:\mathrm{unswered} \\ $$ Answered by EDWIN88 last updated on…
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Question Number 919 by sai dinesh last updated on 24/Apr/15 $$−+−+−=\mathrm{30} \\ $$$${you}\:{can}\:{use}\:{this}\:{numbers}\left(\mathrm{1},\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{9},\mathrm{11},\mathrm{13},\mathrm{15}\right) \\ $$$${you}\:{also}\:{use}\:{a}\:{number}\:{double} \\ $$$${only}\:{genius}\:{is}\:{solve}\:{it} \\ $$$$ \\ $$ Answered by prakash jain…
Question Number 131991 by mnjuly1970 last updated on 10/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:\:\:\:\:\:\:{calculus}…\:\: \\ $$$$\:\:{prove}\:\:{that}\:: \\ $$$$\:\:\phi_{\mathrm{1}} =\int_{\mathrm{0}} ^{\:\mathrm{1}} {li}_{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)=\frac{\pi^{\mathrm{2}} }{\mathrm{2}}\:−\mathrm{4} \\ $$$$\:\:\:\:\phi_{\mathrm{2}} =\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{log}\left(\mathrm{1}−{t}\right)}{{t}^{\frac{\mathrm{3}}{\mathrm{4}}}…