Student[MultivariateCalculus][TaylorApproximation] - return the Taylor series for a multivariate function
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Calling Sequence
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TaylorApproximation(f(x,y,...), [x,y,...]=[a,b,...], order, x=xmin..xmax, y=ymin..ymax, ..., opts)
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Parameters
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f(x, y, ...)
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algebraic expression
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x, y, ...
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name; specify the independent variables
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a, b, ...
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name or real constants; point around which the function is expanded
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order
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(optional) positive integer; order of taylor polynomial
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xmin, xmax, ymin, ymax, ...
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(optional) real constants specifying range over which to plot function
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opts
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(optional) equation(s) of the form option=value where option is one of centeroptions, functionoptions, output, showcenter, showfunction, tayloroptions; specify output options
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Description
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The TaylorApproximation command returns the Taylor approximation of f of a specified order around a specified point. By using options, you can specify that the command returns a plot or animation. This feature is only available if one or two variables are specified.
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The opts argument can contain any of the following equations that set output options. Plotting is only available for univariate or bivariate functions.
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Specifies the plot options for plotting the point or . For more information on plotting options, see plot3d/options.
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Specifies the plot options for plotting the function . For more information on plotting options, see plot3d/options.
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output = value, plot, or animation
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This option controls the return value of the function.
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* output = value specifies that the value of the approximation is returned. Plot options are ignored if output = value. The default is output = value.
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* output = plot specifies that a plot displays, which shows the expression and the Taylor approximation to the function.
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* output = animation specifies that an animation displays, which shows the Taylor approximation approaching the function as the order of the Taylor series increases with each frame.
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showcenter = true or false
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Determines whether the point around which the series is expanded is plotted. The default is true.
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showfunction = true or false
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Determines whether the function f is plotted. The default is true.
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Specifies the plot options for plotting the Taylor approximation to f. The default is . For more information on plotting options, see plot3d/options.
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The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption , see plot/typesetting.
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The default title is constructed from the parameters and the command options. title = "" disables the default title. For more information about specifying a title, see plot/typesetting.
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For information on how to change the default colors, see the Student[SetColors] help page.
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Examples
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>
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>
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The command to create the plot in the Plotting Guide is
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