Taylor Approximation of a Multivariate Function - Maple Programming Help

Taylor Approximation of a Multivariate Function

 Description Calculate the Taylor approximation of a specified degree for a multivariate function.

Enter the function.

 > $f:=\left(x,y\right)\to \left({{x}}^{{3}}{+}{\mathrm{sin}}\left({y}\right)\right)$
 ${f}{:=}\left({x}{,}{y}\right){→}{{x}}^{{3}}{+}{\mathrm{sin}}{}\left({y}\right)$ (1)

Specify an expansion point and order, and then calculate the Taylor approximation.

 > $\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{TaylorApproximation}\right]\left(f\left(x,y\right),\left[x,y\right]=\left[{1}{,}{0}\right],'{5}'\right)$
 $\frac{{1}}{{120}}{}{{y}}^{{5}}{-}\frac{{1}}{{6}}{}{{y}}^{{3}}{+}{3}{}{x}{+}{y}{-}{2}{+}{3}{}{\left({x}{-}{1}\right)}^{{2}}{+}{\left({x}{-}{1}\right)}^{{3}}$ (2)

Alternatively, you can use the Taylor Series tutor, a point-and-click interface. There are two ways to launch this tutor.

 • From the Tools menu, select Tutors, Calculus - Multivariate and then Taylor Series.
 • Enter a multivariate function below, then click the following Taylor Series button.
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