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Category: Algebra

If-f-x-x-x-1-critical-points-

Question Number 190303 by mnjuly1970 last updated on 31/Mar/23 $$ \\ $$$$\:\:\:\:\:\mathrm{I}{f},\:\:{f}\left({x}\right)=\:\frac{\lfloor−{x}\:\rfloor}{{x}}\:+\mathrm{1}\:\:\Rightarrow\:\:{critical}\:{points}\:\:=\:? \\ $$$$ \\ $$ Answered by mehdee42 last updated on 31/Mar/23 $$\mathbb{Z}\cup\left(−\mathrm{1},\mathrm{0}\right) \\…

Question-190297

Question Number 190297 by Shrinava last updated on 31/Mar/23 Answered by Frix last updated on 31/Mar/23 $$\mathrm{Let}\:{u}=\mathrm{cos}\:{x}\:\wedge{v}=\mathrm{sin}\:{x} \\ $$$$\mathrm{Transforming}\:\mathrm{leads}\:\mathrm{to} \\ $$$${u}^{\mathrm{6}} +\mathrm{2}{u}^{\mathrm{3}} {v}^{\mathrm{3}} +\mathrm{2}{u}^{\mathrm{2}} {v}^{\mathrm{2}}…

Question-124740

Question Number 124740 by ajfour last updated on 05/Dec/20 Commented by ajfour last updated on 05/Dec/20 $${Find}\:{eq}.\:{of}\:{circle}\:{passing}\:{through} \\ $$$${intersection}\:{points}\:{of}\:\:{curves} \\ $$$${y}={x}^{\mathrm{2}} −\mathrm{1}\:\:{and}\:\:{y}=\frac{{c}}{{x}}\:;\:\:\:\left({c}\:<\:\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}}\right) \\ $$ Answered…

Find-the-value-of-i-n-for-every-positive-integer-n-where-i-2-1-i-3-i-2-i-i-4-i-2-i-2-etc-

Question Number 190275 by aye786naing last updated on 30/Mar/23 $$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{i}^{\mathrm{n}} \:\mathrm{for}\:\mathrm{every}\:\mathrm{positive} \\ $$$$\:\mathrm{integer}\:\mathrm{n},\:\mathrm{where}\:\mathrm{i}^{\mathrm{2}} \:=\:−\mathrm{1},\:\mathrm{i}^{\mathrm{3}} =\:\mathrm{i}^{\mathrm{2}} \mathrm{i},\:\mathrm{i}^{\mathrm{4}} \:=\:\mathrm{i}^{\mathrm{2}} \mathrm{i}^{\mathrm{2}} \:,\:{etc}. \\ $$ Answered by Frix last…

show-that-a-b-a-ab-b-is-a-monoid-when-G-Z-

Question Number 190241 by astridmei last updated on 30/Mar/23 $${show}\:{that}\:{a}\circledast{b}={a}+{ab}+{b}\:{is}\:{a}\:{monoid}\:{when}\:{G}={Z} \\ $$ Answered by mehdee42 last updated on 30/Mar/23 $$\ast:\mathbb{Z}×\mathbb{Z}\rightarrow\mathbb{Z}\:\:;\:{a}\ast{b}={a}+{b}+{ab} \\ $$$$\left(\mathbb{Z},\ast\right)\:{is}\:{monoid}\:{whenever} \\ $$$$\left.\mathrm{1}\right)\forall{a},{b}\in\mathbb{Z}\:\rightarrow{a}\ast{b}\in\mathbb{Z} \\…