Question Number 2000 by Yozzi last updated on 29/Oct/15 $${Find}\:{a}\:{non}−{constant}\:{function}\:{f}\: \\ $$$${satisfying}\:{f}\left(\mathrm{0}\right)=\mathrm{1},{f}\left(−\mathrm{2}\right)=\mathrm{0}\:{and} \\ $$$${f}\left({x}−{y}\right)={f}\left({x}\right){f}\left({y}\right)−{f}\left(−\mathrm{2}−{x}\right){f}\left({y}−\mathrm{2}\right). \\ $$ Commented by prakash jain last updated on 29/Oct/15 $${x}=\mathrm{0}…
Question Number 133069 by Dwaipayan Shikari last updated on 18/Feb/21 Commented by Dwaipayan Shikari last updated on 18/Feb/21 $${One}\:{can}\:{stretch}\:{and}\:{reform}\:{sides}\:{AB}\:\:{and}\:{AC}\:,\:{by}\: \\ $$$${considering}\:{length}\:\:{BC}\:{as}\:{constant}.\:{the}\:{angle}\: \\ $$$$\phi\:{can}\:{change}.\:{Find}\:{the}\:{relationship}\:{of}\:{changes}\:{between}\:{Side}\: \\ $$$${AB}\:,\:{AC}\:{and}\:{angle}\:\phi…
Question Number 67534 by mathmax by abdo last updated on 28/Aug/19 $${find}\:{the}\:{value}\:{of}\:\:\prod_{{n}=\mathrm{2}} ^{\infty} \:\frac{{n}^{\mathrm{3}} −\mathrm{1}}{{n}^{\mathrm{3}} \:+\mathrm{1}} \\ $$$${and}\:\prod_{{n}=\mathrm{1}} ^{\infty} \left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right) \\ $$ Commented by…
Question Number 1999 by Fitrah last updated on 29/Oct/15 $${if}\: \\ $$$$\left(\mathrm{1}\:+\:{tan}\:\mathrm{1}°\right)\left(\mathrm{1}\:+\:{tan}\:\mathrm{2}°\right)\left(\mathrm{1}\:+\:{tan}\:\mathrm{3}°\right)…… \\ $$$$\left…..\right)\left(\mathrm{1}\:+\:{tan}\:\mathrm{44}°\right)\left(\mathrm{1}\:+\:{tan}\:\mathrm{45}°\right)\overset{} {\:}=\:\:\left\{\:\:\:\sqrt[{\mathrm{3}}]{\left(\sqrt{\mathrm{50}}\:+\:\mathrm{7}\right)}\:−\:\sqrt[{\mathrm{3}}]{\left(\sqrt{\mathrm{50}}−\mathrm{7}\right)}\:\overset{\left({x}\:−\:\mathrm{7}\right)} {\right\}} \\ $$$$\: \\ $$$${find}\:{x}\:=\:…? \\ $$ Answered by Yozzi…
Question Number 133068 by mnjuly1970 last updated on 18/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{advanced}…..{calculus}…. \\ $$$$\:\:\:{evaluation}::\:\underset{{k}=\mathrm{2}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{k}} \left(\:\frac{\zeta\left({k}\right)−\mathrm{1}}{{k}}\right) \\ $$$$\:\:\:\::::\boldsymbol{\Phi}=\underset{{k}=\mathrm{2}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{k}} \:\frac{\zeta\left({k}\right)−\mathrm{1}}{{k}} \\ $$$$\:\:\:\:\:\:\:\:\:=\underset{{k}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}}\:\underset{{n}=\mathrm{2}}…
Question Number 67535 by mr W last updated on 28/Aug/19 Commented by mr W last updated on 28/Aug/19 $${find}\:{the}\:{area}\:{of}\:{the}\:{square}\:{A}=? \\ $$ Commented by Prithwish sen…
Question Number 67532 by mathmax by abdo last updated on 28/Aug/19 $${prove}\:{that}\:\:\pi\:{cotan}\left(\pi\alpha\right)\:={lim}_{{n}\rightarrow+\infty} \:\:\:\sum_{{k}=−{n}} ^{{n}} \:\:\frac{\mathrm{1}}{\alpha−{k}} \\ $$ Commented by ~ À ® @ 237 ~…
Question Number 1997 by prakash jain last updated on 29/Oct/15 $${A}=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…. \\ $$$${B}=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…. \\ $$$${A}−{B}=? \\ $$ Commented by Rasheed Soomro last updated on 30/Oct/15…
Question Number 67533 by mathmax by abdo last updated on 28/Aug/19 $${find}\:{the}\:{value}\:{of}\:\prod_{{n}=\mathrm{1}} ^{\infty} \left(\mathrm{1}+\frac{\mathrm{1}}{{n}\left({n}+\mathrm{2}\right)}\right) \\ $$$$\prod_{{n}=\mathrm{1}} ^{\infty} \left(\mathrm{1}−\frac{\mathrm{2}}{{n}\left({n}+\mathrm{1}\right)}\right) \\ $$ Terms of Service Privacy Policy…
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Question Number 1996 by 123456 last updated on 28/Oct/15 $$\mathrm{given}\:{x},{y}\:\mathrm{continuous}\:\mathrm{and}\:\mathrm{differenriable} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$$\begin{cases}{{x}={x}\left({t}\right)}\\{{y}={y}\left({t}\right)}\end{cases} \\ $$$$\mathrm{does} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\frac{\frac{{d}^{\mathrm{2}} {y}}{{dt}^{\mathrm{2}} }}{\frac{{d}^{\mathrm{2}} {x}}{{dt}^{\mathrm{2}} }}? \\…