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Author: Tinku Tara

1-simplify-S-n-x-k-0-n-C-n-k-cos-k-x-cos-kx-2-find-the-value-of-A-n-k-0-n-C-n-k-cos-k-pi-n-cos-kpi-n-

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}}…

a-n-m-m-n-0-na-n-m-1-m-m-n-gt-0-m-0-na-n-m-m-1-m-m-2-n-gt-0-m-gt-0-a-5-5-a-10-10-

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}…

f-x-y-z-x-y-z-g-x-y-z-x-y-z-h-x-y-z-g-x-y-z-f-x-y-z-h-x-y-z-h-x-y-z-

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…

1-calculate-by-residus-method-0-dx-1-x-2-3-2-find-the-value-of-0-1-1-x-4-1-x-2-3-dx-

Question Number 66459 by mathmax by abdo last updated on 15/Aug/19 $$\left.\mathrm{1}\right)\:{calculate}\:{by}\:{residus}\:{method}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} } \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{1}+{x}^{\mathrm{4}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} }{dx} \\ $$…

find-the-fourier-serie-of-f-t-sinh-t-into-the-interval-1-1-

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}…

30-you-can-use-this-numbers-1-3-5-7-9-11-13-15-you-also-use-a-number-double-only-genius-is-solve-it-

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…

nice-calculus-prove-that-1-0-1-li-2-1-x-2-pi-2-2-4-2-0-1-log-1-t-t-3-4-1-t-dt-pi-3-2-2-2-3-4-log-2-pi-2-hi

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}}}…