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Category: Differentiation

calculate-the-k-th-order-Taylor-polynomials-T-p-k-f-for-the-following-f-x-e-x-1-x-for-p-1-and-k-5-f-x-y-4sin-x-2-y-for-p-0-0-and-k-4-f-x-y-x-3-2xy-e-xy-for-p-1-1-and-k

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} \\…

the-temperature-of-a-fluid-in-heating-unit-of-a-plant-is-given-by-T-x-y-z-100-z-3-10-x-1-2-y-2-2-find-the-minimum-and-maximum-temperatures-if-the-heat-exchanging-components-have-the-s

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}}…

find-and-classify-the-stationary-points-of-f-x-y-x-1-2-y-2-x-2y-xy-4-

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:…

use-the-method-of-lagrange-multipliers-to-fond-the-extrema-of-f-x-y-z-24x-2-y-2-6-z-2-subject-to-z-x-2-y-2-2xy-

Question Number 131690 by LYKA last updated on 07/Feb/21 $${use}\:{the}\:{method}\:{of}\: \\ $$$$\boldsymbol{{lagrange}}\:\boldsymbol{{multipliers}}\:\boldsymbol{{to}}\:\boldsymbol{{fond}}\: \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{extrema}}\:\boldsymbol{{of}}\: \\ $$$$\boldsymbol{{f}}\left(\boldsymbol{{x}}.\boldsymbol{{y}}.\boldsymbol{{z}}\right)=\mathrm{24}\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{y}}^{\mathrm{2}} \left(\mathrm{6}−\boldsymbol{{z}}^{\mathrm{2}} \right) \\ $$$$\boldsymbol{{subject}}\:\boldsymbol{{to}}\:\boldsymbol{{z}}=\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{xy}} \\ $$$$…

What-is-the-maximum-area-of-ellipse-x-2-a-2-y-2-b-2-1-which-touches-the-line-y-3x-2-

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…

differentiate-y-10-1-sin-2-3x-

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}}…