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Find-all-solutions-of-x-real-numbers-such-that-2x-2-7x-6-15-1-x-x-

Question Number 64533 by naka3546 last updated on 19/Jul/19 $${Find}\:\:{all}\:\:{solutions}\:\:{of}\:\:{x}\:\:{real}\:\:{numbers}\:\:{such}\:\:{that} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} \:−\:\mathrm{7}{x}\:+\:\mathrm{6}\:\:=\:\:\mathrm{15}\:\lfloor\frac{\mathrm{1}}{{x}}\rfloor\lfloor{x}\rfloor \\ $$ Answered by MJS last updated on 19/Jul/19 $${x}=\mathrm{0}\:\Rightarrow\:\lfloor\frac{\mathrm{1}}{{x}}\rfloor\:\mathrm{not}\:\mathrm{defined} \\ $$$$…

what-is-fractional-derivative-

Question Number 129998 by Eric002 last updated on 21/Jan/21 $${what}\:{is}\:{fractional}\:{derivative}? \\ $$ Answered by Olaf last updated on 21/Jan/21 $$\mathrm{Generalization}\:\mathrm{of}\:\mathrm{the}\:\mathrm{derivative} \\ $$$$\mathrm{for}\:\alpha\:\in\mathbb{R}\::\:{D}^{\alpha} {f}\:=\:{f}^{\left(\alpha\right)} \left({x}\right) \\…

prove-that-cos-n-sin-n-n-converge-sequence-

Question Number 129997 by mohammad17 last updated on 21/Jan/21 $${prove}\:{that}\:\left[\left({cos}\left({n}\right)+{sin}\left({n}\right)\right)/{n}\right]\:{converge}\:{sequence} \\ $$ Answered by Dwaipayan Shikari last updated on 21/Jan/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cosn}+{sinn}}{{n}}=\frac{\mathrm{1}}{\mathrm{2}}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{e}^{{in}}…

Question-129955

Question Number 129955 by mohammad17 last updated on 21/Jan/21 Answered by Olaf last updated on 21/Jan/21 $$\mathrm{A}\:=\:\begin{bmatrix}{\mathrm{1}}&{\mathrm{1}}&{−\mathrm{15}}&{\mathrm{4}}\\{\mathrm{16}}&{−\mathrm{2}}&{−\mathrm{3}}&{\mathrm{1}}\\{\mathrm{1}}&{−\mathrm{1}}&{\mathrm{3}}&{\mathrm{17}}\\{\mathrm{2}}&{−\mathrm{14}}&{\mathrm{3}}&{\mathrm{2}}\end{bmatrix} \\ $$$$\mathrm{det}\left(\mathrm{A}\right)\:=\:−\mathrm{56460}\:\neq\:\mathrm{0} \\ $$$$\mathrm{A}_{\mathrm{1}} \:=\:\begin{bmatrix}{−\mathrm{2}}&{\mathrm{1}}&{−\mathrm{15}}&{\mathrm{4}}\\{\mathrm{2}}&{−\mathrm{2}}&{−\mathrm{3}}&{\mathrm{1}}\\{\mathrm{9}}&{−\mathrm{1}}&{\mathrm{3}}&{\mathrm{17}}\\{−\mathrm{8}}&{−\mathrm{14}}&{\mathrm{3}}&{\mathrm{2}}\end{bmatrix} \\ $$$$\mathrm{det}\left(\mathrm{A}_{\mathrm{1}} \right)\:=\:−\mathrm{14115}…

Question-64384

Question Number 64384 by aliesam last updated on 17/Jul/19 Answered by MJS last updated on 17/Jul/19 $$\left({y}={x}\right)\cap\left({y}=\frac{{x}}{\mathrm{8}}\right)=\begin{pmatrix}{\mathrm{0}}\\{\mathrm{0}}\end{pmatrix} \\ $$$$\left({y}={x}\right)\cap\left({y}=\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)=\begin{pmatrix}{\mathrm{1}}\\{\mathrm{1}}\end{pmatrix} \\ $$$$\:\:\:\:\:\left[{x}=\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:\Rightarrow\:{x}^{\mathrm{3}} =\mathrm{1}\:\Rightarrow\:{x}=\mathrm{1}\right] \\…