Question Number 66211 by mr W last updated on 10/Aug/19 Commented by mr W last updated on 10/Aug/19 $${Find}\:{the}\:{maximum}\:{area}\:{of}\:{a}\:{right} \\ $$$${triangle}\:{inscribed}\:{in}\:{an}\:{ellipse}. \\ $$ Commented by…
Question Number 672 by 123456 last updated on 21/Feb/15 $${if}\:{a}_{{n}} ,{b}_{{n}} ,{c}_{{n}} \:{are}\:{real}\:{sequence}\:{with} \\ $$$${a}_{{n}} >\mathrm{0},{b}_{{n}} >\mathrm{0},{c}_{{n}} >\mathrm{0} \\ $$$${and} \\ $$$${a}_{{n}} ^{{n}} <{b}_{{n}} <{c}_{{n}}…
Question Number 131743 by frc2crc last updated on 08/Feb/21 $$\underset{{C}:\mid{z}\mid=\mathrm{1}} {\int}\frac{−\mathrm{2}{i}}{{Az}^{\mathrm{2}} +\mathrm{2}{z}+{A}}{dz}\:{where}\:{C}\:{is}\:{a}\:{unit}\:{circle}\:{with}\:{radius}\:\mathrm{1} \\ $$ Answered by mathmax by abdo last updated on 08/Feb/21 $$\mathrm{let}\:\varphi\left(\mathrm{z}\right)=\frac{−\mathrm{2i}}{\mathrm{az}^{\mathrm{2}} \:+\mathrm{2z}+\mathrm{a}}\:\mathrm{poles}\:\mathrm{of}\:\varphi?…
Question Number 669 by 112358 last updated on 21/Feb/15 $${Given}\:{only}\:{the}\:{standard}\:{result}\:\underset{{r}=\mathrm{1}} {\overset{{N}} {\sum}}{r}^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{6}}{N}\left({N}+\mathrm{1}\right)\left(\mathrm{2}{N}+\mathrm{1}\right)\: \\ $$$${is}\:{applied}\:{to}\:{determining}\:{the}\:{series} \\ $$$$\mathrm{1}^{\mathrm{2}} +\mathrm{2}×\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +\mathrm{2}×\mathrm{4}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} +\mathrm{2}×\mathrm{6}^{\mathrm{2}} +\mathrm{7}^{\mathrm{2}} +…+\mathrm{2}\left({n}−\mathrm{1}\right)^{\mathrm{2}} +{n}^{\mathrm{2}}…
Question Number 131733 by LYKA last updated on 07/Feb/21 $$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{minimum}}\:\boldsymbol{{distance}} \\ $$$$\boldsymbol{{between}}\:\boldsymbol{{the}}\:\boldsymbol{{point}}\:\left(\mathrm{1},\mathrm{1},\mathrm{1}\right)\:{and} \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{plane}}\:\boldsymbol{{x}}+\mathrm{2}\boldsymbol{{y}}+\mathrm{3}\boldsymbol{{z}}=\mathrm{6} \\ $$$$ \\ $$ Answered by physicstutes last updated on 07/Feb/21…
Question Number 131732 by mnjuly1970 last updated on 07/Feb/21 $$\:\:\:{prove}\:{that}: \\ $$$$\:\: \\ $$$$\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2}{n}−\mathrm{1}\right)\left({e}^{\left(\mathrm{2}{n}−\mathrm{1}\right)\pi} −{e}^{−\left(\mathrm{2}{n}−\mathrm{1}\right)\pi} \right)}=\frac{{ln}\left(\mathrm{2}\right)}{\mathrm{16}} \\ $$$$\: \\ $$ Terms of Service…
Question Number 66199 by aliesam last updated on 10/Aug/19 $${calculate} \\ $$$${cos}\left(\mathrm{79}\right)=? \\ $$ Commented by $@ty@m123 last updated on 10/Aug/19 $${Use}\:{trigonometrical}\:{table}. \\ $$$${OR}\: \\…
Question Number 131735 by LYKA last updated on 07/Feb/21 $${calculate}\:{the}\:{k}-{th}\:{order}\:{Taylor} \\ $$$${polynomials}\:{T}_{{p}} ^{{k}} {f}\:{for}\:{the}\:{following} \\ $$$$ \\ $$$${f}\left({x}\right)=\frac{{e}^{−{x}} }{\mathrm{1}+{x}}\:\:\:{for}\:{p}=−\mathrm{1}\:{and}\:{k}=\mathrm{5} \\ $$$$ \\ $$$${f}\left({x}.{y}\right)=\:\mathrm{4}{sin}\left({x}^{\mathrm{2}} +{y}\right)\:{for}\:{p}=\left(\mathrm{0},\mathrm{0}\right)\:{and} \\…
Question Number 131734 by LYKA last updated on 07/Feb/21 $$\boldsymbol{{given}}\:\boldsymbol{{the}}\:\boldsymbol{{function}} \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}.\boldsymbol{{y}}\right)=\boldsymbol{{xy}}\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{y}}−\mathrm{1}\right) \\ $$$$\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{f}}\left(\boldsymbol{{x}}.\boldsymbol{{y}}\right)\:\boldsymbol{{has}}\:\boldsymbol{{some}}\:\left(\mathrm{0},\mathrm{1}\right) \\ $$$$\boldsymbol{{as}}\:\boldsymbol{{a}}\:\boldsymbol{{stationery}}\:\boldsymbol{{point}} \\ $$$$ \\ $$$$\boldsymbol{{use}}\:\boldsymbol{{tylor}}\:\boldsymbol{{series}}\:\boldsymbol{{method}}\:\boldsymbol{{to}}\: \\ $$$$\boldsymbol{{determine}}\:\boldsymbol{{whether}}\:\left(\mathrm{0}.\mathrm{1}\right)\:\boldsymbol{{is}}\:\boldsymbol{{a}} \\ $$$$\boldsymbol{{minima}}\:,\boldsymbol{{maxima}}\:\boldsymbol{{or}}\:\boldsymbol{{saddle}}\: \\…
Question Number 66197 by Rasheed.Sindhi last updated on 11/Aug/19 $$\mathrm{If}\:\:\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}=\mathrm{1},\mathrm{prove}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{x}^{\mathrm{n}} +\mathrm{x}^{\mathrm{n}−\mathrm{2}} +\mathrm{x}^{\mathrm{n}−\mathrm{4}} =\mathrm{0} \\ $$ Commented by mr W last updated on 10/Aug/19…