Question Number 214078 by abdelsalam last updated on 26/Nov/24 Answered by a.lgnaoui last updated on 28/Nov/24 $$\mathrm{une}\:\mathrm{matrice}\:\left(\mathrm{4}×\mathrm{3}\right)\mathrm{impossible}\:\mathrm{a}\:\mathrm{determiner}\: \\ $$$$\mathrm{son}\:\mathrm{determinant}\:\:\: \\ $$ Commented by abdelsalam last…
Question Number 214072 by Mwamba last updated on 26/Nov/24 Answered by TonyCWX08 last updated on 27/Nov/24 Answered by TonyCWX08 last updated on 27/Nov/24 $${Consider}\:{two}\:{points},\:{P}\:{and}\:{Q}. \\…
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Question Number 214050 by CrispyXYZ last updated on 25/Nov/24 $$\mathrm{If}\:{A}:\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:…,\:{a}_{\mathrm{62}} \:\mathrm{and}\:{B}:\:{b}_{\mathrm{1}} ,\:{b}_{\mathrm{2}} ,\:…,\:{b}_{\mathrm{62}} \:\mathrm{are}\:\mathrm{two} \\ $$$$\mathrm{strictly}\:\mathrm{increasing}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{sequences} \\ $$$$\mathrm{such}\:\mathrm{that}\:{a}_{\mathrm{62}} \leqslant\mathrm{755}\:\mathrm{and}\:{b}_{\mathrm{62}} \leqslant\mathrm{755}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{of}\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{62}}…
Question Number 213999 by issac last updated on 24/Nov/24 $$\int\int…\int_{\:\mathcal{D}} \:\:{e}^{−\left({z}_{\mathrm{1}} ^{\mathrm{2}} +{z}_{\mathrm{2}} ^{\mathrm{2}} …+{z}_{{n}} ^{\mathrm{2}} \right)} \mathrm{da} \\ $$$$\mathcal{D}=\underset{\boldsymbol{\mathrm{n}}\:\boldsymbol{\mathrm{times}}} {\left[\mathrm{0},\infty\right)×\left[\mathrm{0},\infty\right)……\left[\mathrm{0},\infty\right)} \\ $$$$\int_{\mathrm{0}} ^{\:\pi} \:{e}^{−\mathrm{sin}^{\mathrm{2}}…
Question Number 213948 by issac last updated on 22/Nov/24 $$\mathrm{evaluate}. \\ $$$$\mathrm{1}.\:\frac{\mathrm{1}}{\pi}\int_{\mathrm{0}} ^{\:\pi} \:\:{e}^{−\boldsymbol{{i}}\left({t}−\mathrm{sin}\left({t}\right)\right)} \mathrm{d}{t} \\ $$$$\mathrm{2}.\:\int_{\mathrm{0}} ^{\:\mathrm{a}} \int_{\mathrm{0}} ^{\:\mathrm{a}} \:\:\sqrt{{u}^{\mathrm{2}} +{v}^{\mathrm{2}} −\mathrm{6}{u}+\mathrm{9}}\:\mathrm{d}{u}\mathrm{d}{v} \\ $$$$\mathrm{3}.\:\int_{\mathrm{0}}…
Question Number 213893 by issac last updated on 21/Nov/24 $$\int_{\:−\pi} ^{\:\:\pi} \:\:\frac{\mathrm{d}{z}}{\mathrm{1}+\mathrm{3cos}^{\mathrm{2}} \left({z}\right)}=¿¿\:\:\: \\ $$ Commented by BHOOPENDRA last updated on 21/Nov/24 $$\pi??? \\ $$…
Question Number 213877 by issac last updated on 20/Nov/24 $$\mathrm{evaluate}. \\ $$$$\int_{−\pi} ^{\:+\pi} \:\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{3cos}^{\mathrm{2}} \left({z}\right)}\:\mathrm{d}{z} \\ $$$$\mathrm{real}\:\mathrm{analysis}\:\mathrm{method}: \\ $$$$\mathrm{complex}\:\mathrm{analysis}\:\mathrm{method}: \\ $$ Terms of Service Privacy…
Question Number 213871 by 073 last updated on 19/Nov/24 Commented by Frix last updated on 20/Nov/24 $$\mathrm{Elliptic}\:\mathrm{Integral}: \\ $$$$\mathrm{4}\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\sqrt{{a}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \:{x}\:+{b}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \:{x}}\:{dx}\:=\mathrm{4}{a}\mathrm{E}\:\frac{{a}^{\mathrm{2}}…
Question Number 213862 by issac last updated on 19/Nov/24 $$\mathrm{Help}\:\mathrm{me}…..!!!\:\::\left(\:\:\right. \\ $$$$\mathrm{complex}\:\mathrm{anaylsis}\:\mathrm{problem}.. \\ $$$${f}\left({z}\right)\:\mathrm{is}\:\mathrm{entire}\:\mathrm{in}\:\mathrm{path}\:{C}\: \\ $$$$\mathrm{entire}:\:\mathrm{Differantiable}\:\mathrm{complex}\:\mathrm{function} \\ $$$$\mathrm{mean}\:{f}\left({z}\right)\:\mathrm{satisfy}\:{f}\left({z}\right)={u}\left({x},{y}\right)+\boldsymbol{{i}}\centerdot{v}\left({x},{y}\right)\:\: \\ $$$$\frac{\partial{u}}{\partial{x}}=−\frac{\partial{v}}{\partial{y}}\:\mathrm{or}\:\:\frac{\partial{u}}{\partial{y}}=−\frac{\partial{v}}{\partial{x}}\:\left(\mathrm{couchy}-\mathrm{riemann}\right) \\ $$$$\mathrm{show}\:\mathrm{that}\:\int_{\:{C}} \:\frac{{f}\left({z}\right)}{{f}'\left({z}\right)}\:\mathrm{d}{z}=\mathrm{2}\pi\boldsymbol{{i}}\underset{{h}=\mathrm{1}} {\overset{{M}} {\sum}}\:{P}_{{h}}…