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Give-the-function-f-x-x-1-x-2-2-x-3-3-x-4-4-x-2022-2022-Find-extremes-of-f-x-

Question Number 196710 by tri26112004 last updated on 30/Aug/23 $${Give}\:{the}\:{function}: \\ $$$${f}\left({x}\right)=\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)^{\mathrm{2}} \left({x}−\mathrm{3}\right)^{\mathrm{3}} \left({x}−\mathrm{4}\right)^{\mathrm{4}} …\left({x}−\mathrm{2022}\right)^{\mathrm{2022}} \\ $$$${Find}\:{extremes}\:{of}\:{f}\left({x}\right)¿ \\ $$ Commented by mr W last updated…

Question-196682

Question Number 196682 by sonukgindia last updated on 29/Aug/23 Answered by mr W last updated on 28/Sep/23 $$\mathrm{0}.\mathrm{006}×\mathrm{0}.\mathrm{98}+\mathrm{0}.\mathrm{994}×\mathrm{0}.\mathrm{8}=\mathrm{0}.\mathrm{81\%}\:\checkmark \\ $$ Terms of Service Privacy Policy…

lim-n-n-2-2ncos-k-1-2ne-i-k-d-

Question Number 196705 by josemate19 last updated on 29/Aug/23 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{−\infty} {\overset{\:\:\:\:\infty} {\int}}\frac{{n}!\mathrm{2}^{\mathrm{2}{ncos}\left(\phi\right)} }{\underset{{k}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{2}{ne}^{{i}\phi} −{k}\right)}{d}\phi \\ $$ Terms of Service Privacy Policy Contact:…

Question-196637

Question Number 196637 by sonukgindia last updated on 28/Aug/23 Answered by AST last updated on 28/Aug/23 $${a}=\sqrt{\mathrm{12}−\sqrt{{m}}};{b}=\sqrt{\mathrm{12}+\sqrt{{m}}},{a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{24} \\ $$$${ab}=\sqrt{\mathrm{144}−{m}};\left({a}+{b}\right)^{\mathrm{2}} =\mathrm{24}+\mathrm{2}\sqrt{\mathrm{144}−{m}} \\ $$$$\Rightarrow{a}+{b}=\sqrt{\mathrm{24}+\mathrm{2}\sqrt{\mathrm{144}−{m}}}={n} \\…

Question-196635

Question Number 196635 by sonukgindia last updated on 28/Aug/23 Answered by sniper237 last updated on 28/Aug/23 $$=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} {f}\left({n}\right)\:;\:{f}\left({z}\right)=\frac{\mathrm{1}}{\left(\mathrm{2}{z}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$$$\overset{{Residu}\:{theo}\:{applicat\%}} {=}\:{Res}\left(\frac{\pi{f}\left({z}\right)}{{sin}\left(\pi{z}\right)};\:−\mathrm{1}/\mathrm{2}\right)\:\:\: \\…

Prove-that-x-3-y-6-20-has-no-positive-integer-solution-

Question Number 196650 by CrispyXYZ last updated on 28/Aug/23 $$\mathrm{Prove}\:\mathrm{that}\:{x}^{\mathrm{3}} ={y}^{\mathrm{6}} +\mathrm{20}\:\mathrm{has}\:\mathrm{no}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{solution}. \\ $$ Answered by AST last updated on 28/Aug/23 $${x}^{\mathrm{3}} \equiv\mathrm{1},−\mathrm{1}\:{or}\:\mathrm{0}\left({mod}\:\mathrm{9}\right) \\ $$$${when}\:\left({y},\mathrm{9}\right)=\mathrm{1};{y}^{\mathrm{6}}…