Question Number 153392 by ArielVyny last updated on 06/Sep/21 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{{a}} =?\:\:\: \\ $$ Commented by prakash jain last updated on 07/Sep/21 $$\zeta\left(−{a}\right)−\zeta\left(−{a},{n}+\mathrm{1}\right) \\…
Question Number 153395 by Rankut last updated on 07/Sep/21 $${given}\:{that}\:\:{f}\left({x}\right)=\mathrm{4}{x}^{\mathrm{3}} −\mathrm{48}{x}.\:{find}\: \\ $$$${the}\:{stationary}\:{point}\:{of}\:{f}\left({x}\right) \\ $$ Answered by puissant last updated on 07/Sep/21 $$\frac{\partial}{\partial{x}}{f}\left({x}\right)=\mathrm{0}\:\Rightarrow\:\mathrm{12}{x}^{\mathrm{2}} −\mathrm{48}=\mathrm{0} \\…
Question Number 87854 by jagoll last updated on 06/Apr/20 $$\int\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{x}+\mathrm{2cos}\:\mathrm{x}+\mathrm{3}}\:\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 06/Apr/20 $${I}\:=\int\:\:\frac{{dx}}{\mathrm{2}{cosx}\:+{sinx}\:+\mathrm{3}}\:{we}\:{do}\:{the}\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:\Rightarrow \\ $$$${I}\:=\int\:\:\:\frac{\mathrm{2}{dt}}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\left(\mathrm{2}\frac{\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 22319 by Tinkutara last updated on 15/Oct/17 $$\mathrm{A}\:\mathrm{string}\:\mathrm{of}\:\mathrm{negligible}\:\mathrm{mass}\:\mathrm{going}\:\mathrm{over}\:\mathrm{a} \\ $$$$\mathrm{clamped}\:\mathrm{pulley}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{supports}\:\mathrm{a} \\ $$$$\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:{M}.\:\mathrm{The}\:\mathrm{force}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{pulley}\:\mathrm{by}\:\mathrm{the}\:\mathrm{clamp}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$ Commented by Tinkutara last updated on 15/Oct/17…
Question Number 22316 by Tinkutara last updated on 15/Oct/17 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{{p}} \:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left({a}_{\mathrm{0}} +{a}_{\mathrm{1}} {x}+{a}_{\mathrm{2}} {x}^{\mathrm{2}} +{a}_{\mathrm{3}} {x}^{\mathrm{3}} +…+{a}_{{k}} {x}^{{k}} \right)^{{n}} \\ $$$$\mathrm{is}\:\Sigma\frac{{n}!}{{n}_{\mathrm{0}} !{n}_{\mathrm{1}} !{n}_{\mathrm{2}}…
Question Number 22315 by Tinkutara last updated on 15/Oct/17 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left({x}_{\mathrm{1}} +{x}_{\mathrm{2}} +{x}_{\mathrm{3}} +…+{x}_{{k}} \right)^{{n}} \\ $$$$=\:\frac{{n}!}{\left({q}!\right)^{{k}−{r}} \left[\left({q}+\mathrm{1}\right)!\right]^{{r}} }\:,\:\mathrm{where}\:{n}\:=\:{qk}\:+\:{r}, \\ $$$$\mathrm{0}\:\leqslant\:{r}\:\leqslant\:{k}\:−\:\mathrm{1} \\ $$ Terms…
Question Number 153384 by SANOGO last updated on 06/Sep/21 Answered by mindispower last updated on 06/Sep/21 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\mid\frac{{U}_{{n}+\mathrm{1}} }{{U}_{{n}} }\mid=\mathrm{0} \\ $$$$\Rightarrow\epsilon=\frac{\mathrm{1}}{\mathrm{2}},\exists{N}\in\mathbb{N}\:\forall{n}\geqslant{N}\:\:\mid\frac{{U}_{{n}+\mathrm{1}} }{{U}_{{n}} }\mid\leqslant\frac{\mathrm{1}}{\mathrm{2}} \\…
Question Number 22313 by math solver last updated on 15/Oct/17 Commented by Joel577 last updated on 16/Oct/17 $$\sqrt{\mathrm{5}{x}\:+\:\mathrm{7}}\:−\:\sqrt{\mathrm{3}{x}\:+\:\mathrm{1}}\:=\:\sqrt{{x}\:+\:\mathrm{3}} \\ $$$${x}\:\geqslant\:−\frac{\mathrm{7}}{\mathrm{5}}\:\:\mathrm{and}\:\:{x}\:\geqslant\:−\frac{\mathrm{1}}{\mathrm{3}}\:\:\mathrm{and}\:\:{x}\:\geqslant\:−\mathrm{3} \\ $$$$\Rightarrow\:{x}\:\geqslant\:−\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$ \\…
Question Number 153381 by mathdanisur last updated on 06/Sep/21 $$\mathrm{let}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\geqslant\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{12} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{min}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{S}\:=\:\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:+\:\mathrm{xyz}\:+\:\frac{\mathrm{1}}{\mathrm{xy}\:+\:\mathrm{yz}\:+\:\mathrm{zx}} \\ $$ Commented by mr W last updated…
Question Number 87843 by ar247 last updated on 06/Apr/20 Commented by ar247 last updated on 06/Apr/20 $${please}\:{help}\:{me}\:{with}\:{explenation} \\ $$ Commented by jagoll last updated on…