Question Number 11217 by FilupS last updated on 17/Mar/17 $$\exists{e}_{{i}} :{i}\in\mathbb{N}\:\:\:\:\:\:\:\:{e}_{{i}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{basis}\:\mathrm{vector} \\ $$$$\boldsymbol{{A}}\in\mathbb{C}^{{n}} \\ $$$$\boldsymbol{{A}}=\underset{{i}\in\mathbb{N}} {\sum}{e}_{{i}} {A}_{{i}} =\begin{pmatrix}{{A}_{\mathrm{1}} }\\{{A}_{\mathrm{2}} }\\{\vdots}\\{{A}_{{n}} }\end{pmatrix}\:\:\:=\:\mid{A}\rangle \\ $$$$\langle{B}\mid=\left(\mid{B}^{\ast} \rangle\right)^{\mathrm{T}}…
Question Number 142276 by mohammad17 last updated on 29/May/21 $$\int_{\mathrm{0}} ^{\:\mathrm{2}} \sqrt{\mathrm{1}+{e}^{\mathrm{2}{x}} }{dx} \\ $$ Answered by mathmax by abdo last updated on 29/May/21 $$\mathrm{I}\int_{\mathrm{1}}…
Question Number 142253 by mathdave last updated on 28/May/21 Answered by mr W last updated on 28/May/21 $$\mathrm{3}\:{black} \\ $$$$\mathrm{4}\:{white} \\ $$$$\mathrm{5}\:{red} \\ $$$$\Sigma=\mathrm{12}\:{balls} \\…
Question Number 142252 by Algoritm last updated on 28/May/21 Answered by MJS_new last updated on 29/May/21 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{for}\:{x}\:\mathrm{then}\:\mathrm{insert}\:\mathrm{into}\:\mathrm{the}\:\mathrm{1}^{\mathrm{st}} \\ $$$$\mathrm{let}\:{y}=\mathrm{2arctan}\:{t} \\ $$$$\mathrm{solve}\:\mathrm{for}\:{t} \\ $$$$\mathrm{check}\:\mathrm{all}\:\mathrm{solutions} \\…
Question Number 142236 by mathocean1 last updated on 28/May/21 $$\mathrm{f}\:\mathrm{is}\:\mathrm{an}\:\mathrm{endomorphism}\:\mathrm{of}\:\mathrm{V}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{f}\circ\mathrm{f}=−\mathrm{Id}_{\mathrm{V}} \:. \\ $$$$\mathrm{1}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{f}\:\mathrm{is}\:\mathrm{an}\:\mathrm{isomorphism}\:\mathrm{of} \\ $$$$\mathrm{V}\:\mathrm{and}\:\mathrm{express}\:\mathrm{f}^{−\mathrm{1}} \:\mathrm{in}\:\mathrm{function}\:\mathrm{of}\:\mathrm{f}. \\ $$$$\mathrm{2}.\:\mathrm{show}\:\mathrm{that}\:\overset{\rightarrow} {\mathrm{0}}\:\mathrm{is}\:\mathrm{the}\:\mathrm{one}\:\mathrm{invariant} \\ $$$$\mathrm{vector}\:\mathrm{by}\:\mathrm{f}. \\ $$$$\mathrm{3}.\:\mathrm{Given}\:\overset{\rightarrow}…
Question Number 76696 by benjo 1/2 santuyy last updated on 29/Dec/19 $${what}\:{is}\:{the}\:{value}\:{ln}\left(\mathrm{0}\right).? \\ $$ Answered by john santu last updated on 29/Dec/19 $${ln}\left(\mathrm{0}\right)=−\propto \\ $$$${so}\:{e}^{{ln}\left(\mathrm{0}\right)}…
Question Number 142208 by ZiYangLee last updated on 27/May/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{which}\:\mathrm{is} \\ $$$$\mathrm{orthogonal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{circles}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{7}{x}−{y}=\mathrm{0} \\ $$$$\mathrm{and}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{6}{y}+\mathrm{5}=\mathrm{0}\:\mathrm{and}\:\mathrm{which}\:\mathrm{passes} \\ $$$$\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\left(−\mathrm{3},\mathrm{0}\right). \\ $$ Answered by mr…
Question Number 142205 by mohammad17 last updated on 27/May/21 Commented by mohammad17 last updated on 27/May/21 $${help}\:{me}\:{sir}\:? \\ $$ Commented by mohammad17 last updated on…
Question Number 76667 by naka3546 last updated on 29/Dec/19 Commented by benjo 1/2 santuyy last updated on 29/Dec/19 $${using}\:{L}'{Hopital}\:{Rule}\: \\ $$ Answered by john santu…
Question Number 142185 by mohammad17 last updated on 27/May/21 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}{dx} \\ $$ Answered by MJS_new last updated on 27/May/21 $$\mathrm{I}\:\mathrm{showed}\:\mathrm{this}\:\mathrm{before}… \\ $$$${x}^{\mathrm{4}} +\mathrm{1}=\left({x}^{\mathrm{2}} −\sqrt{\mathrm{2}}{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}}…