Question Number 131734 by LYKA last updated on 07/Feb/21 $$\boldsymbol{{given}}\:\boldsymbol{{the}}\:\boldsymbol{{function}} \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}.\boldsymbol{{y}}\right)=\boldsymbol{{xy}}\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{y}}−\mathrm{1}\right) \\ $$$$\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{f}}\left(\boldsymbol{{x}}.\boldsymbol{{y}}\right)\:\boldsymbol{{has}}\:\boldsymbol{{some}}\:\left(\mathrm{0},\mathrm{1}\right) \\ $$$$\boldsymbol{{as}}\:\boldsymbol{{a}}\:\boldsymbol{{stationery}}\:\boldsymbol{{point}} \\ $$$$ \\ $$$$\boldsymbol{{use}}\:\boldsymbol{{tylor}}\:\boldsymbol{{series}}\:\boldsymbol{{method}}\:\boldsymbol{{to}}\: \\ $$$$\boldsymbol{{determine}}\:\boldsymbol{{whether}}\:\left(\mathrm{0}.\mathrm{1}\right)\:\boldsymbol{{is}}\:\boldsymbol{{a}} \\ $$$$\boldsymbol{{minima}}\:,\boldsymbol{{maxima}}\:\boldsymbol{{or}}\:\boldsymbol{{saddle}}\: \\…
Question Number 131735 by LYKA last updated on 07/Feb/21 $${calculate}\:{the}\:{k}-{th}\:{order}\:{Taylor} \\ $$$${polynomials}\:{T}_{{p}} ^{{k}} {f}\:{for}\:{the}\:{following} \\ $$$$ \\ $$$${f}\left({x}\right)=\frac{{e}^{−{x}} }{\mathrm{1}+{x}}\:\:\:{for}\:{p}=−\mathrm{1}\:{and}\:{k}=\mathrm{5} \\ $$$$ \\ $$$${f}\left({x}.{y}\right)=\:\mathrm{4}{sin}\left({x}^{\mathrm{2}} +{y}\right)\:{for}\:{p}=\left(\mathrm{0},\mathrm{0}\right)\:{and} \\…
Question Number 131717 by LYKA last updated on 07/Feb/21 $${the}\:{temperature}\:{of}\:{a}\:{fluid} \\ $$$${in}\:{heating}\:{unit}\:{of}\:{a}\:{plant}\:{is}\:{given}\:{by} \\ $$$${T}\left({x}.{y}.{z}\right)=\:\frac{\mathrm{100}\left({z}−\mathrm{3}\right)}{\mathrm{10}−\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\left({y}−\mathrm{2}\right)^{\mathrm{2}} } \\ $$$${find}\:{the}\:{minimum}\:{and}\:{maximum}\: \\ $$$${temperatures}\:{if}\:{the}\:{heat}\:{exchanging}\: \\ $$$${components}\:{have}\:{the}\:{shapes}\: \\ $$$${z}=\frac{{x}^{\mathrm{2}} }{\mathrm{4}}−\frac{{y}^{\mathrm{2}}…
Question Number 131718 by LYKA last updated on 07/Feb/21 $$\boldsymbol{{find}}\:\:\boldsymbol{{and}}\:\boldsymbol{{classify}}\:\boldsymbol{{the}}\:\boldsymbol{{stationary}} \\ $$$$\boldsymbol{{points}}\:\boldsymbol{{of}} \\ $$$$\boldsymbol{{f}}\left(\boldsymbol{{x}}.\boldsymbol{{y}}\right)=\left(\boldsymbol{{x}}−\mathrm{1}\right)^{\mathrm{2}} \left(\boldsymbol{{y}}−\mathrm{2}\right)\left(\boldsymbol{{x}}−\mathrm{2}\boldsymbol{{y}}\right)\left(\boldsymbol{{xy}}+\mathrm{4}\right) \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 66183 by 0ister D1Id0 last updated on 10/Aug/19 $$\mathrm{why}\:\underset{{j}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({j}^{\mathrm{2}} {x}\right)}{{j}^{\mathrm{2}} }\:\mathrm{can}'\mathrm{t}\:\mathrm{differantial} \\ $$$$\mathrm{anywhere}??\:\:\mathrm{plz}\:\mathrm{ploof}….\mathrm{help} \\ $$ Commented by mathmax by abdo last…
Question Number 66163 by aliesam last updated on 09/Aug/19 Answered by mr W last updated on 09/Aug/19 $${y}={x}^{{x}^{{x}^{….} } } \\ $$$${y}={x}^{{y}} \\ $$$$\mathrm{ln}\:{y}={y}\:\mathrm{ln}\:{x} \\…
Question Number 622 by 123456 last updated on 12/Feb/15 $$\frac{{y}}{{x}}\left(\frac{{dy}}{{dx}}−\frac{{y}}{{x}}\right)=\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} } \\ $$ Commented by prakash jain last updated on 12/Feb/15 $${y}={kx}? \\ $$…
Question Number 131690 by LYKA last updated on 07/Feb/21 $${use}\:{the}\:{method}\:{of}\: \\ $$$$\boldsymbol{{lagrange}}\:\boldsymbol{{multipliers}}\:\boldsymbol{{to}}\:\boldsymbol{{fond}}\: \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{extrema}}\:\boldsymbol{{of}}\: \\ $$$$\boldsymbol{{f}}\left(\boldsymbol{{x}}.\boldsymbol{{y}}.\boldsymbol{{z}}\right)=\mathrm{24}\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{y}}^{\mathrm{2}} \left(\mathrm{6}−\boldsymbol{{z}}^{\mathrm{2}} \right) \\ $$$$\boldsymbol{{subject}}\:\boldsymbol{{to}}\:\boldsymbol{{z}}=\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{xy}} \\ $$$$…
Question Number 131642 by liberty last updated on 07/Feb/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{area}\: \\ $$$$\mathrm{of}\:\mathrm{ellipse}\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} }+\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }=\mathrm{1}\:\mathrm{which}\:\mathrm{touches} \\ $$$$\mathrm{the}\:\mathrm{line}\:\mathrm{y}\:=\:\mathrm{3x}+\mathrm{2}. \\ $$ Answered by benjo_mathlover last updated…
Question Number 66099 by olalekan2 last updated on 09/Aug/19 $${differentiate}\:{y}=\mathrm{10}^{\mathrm{1}−{sin}^{\mathrm{2}} \mathrm{3}{x}} \\ $$ Commented by mathmax by abdo last updated on 09/Aug/19 $${y}\left({x}\right)\:=\mathrm{10}^{\mathrm{1}−{sin}^{\mathrm{2}} \left(\mathrm{3}{x}\right)} \:\Rightarrow{y}\left({x}\right)\:={e}^{\left(\mathrm{1}−{sin}^{\mathrm{2}}…