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I want to plot the Taylor polynomials of $f(x,y)= Sin(1 + x + y^2)/(4 + x^2 + y^2)$ of degrees 4 and 7 around the point $(0,0)$ over the rectangle $[-\pi,\pi]\times [-\pi,\pi]$

I am currently using

 Series[(Sin(1 + x + y^2))/(4 + x^2 + y^2), {x, 0 , 4}, {y, 0, 7}], 
 {x,-pi, pi} , {y, -pi,pi}]

Nothing actually happens. I also tried just computing the points and then graphing those, but I have quite a few of these plots to do and it seems like a hassle. Anyone have any ideas?

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closed as off-topic by Mr.Wizard Aug 8 at 8:04

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Mr.Wizard
If this question can be reworded to fit the rules in the help center, please edit the question.

Does this give what you expect: Plot3D[Normal@Series[(Sin [1 + x + y^2])/(4 + x^2 + y^2), {x, 0, 4}, {y, 0, 7}] /. {x -> z, y -> w}, {z, -Pi, Pi}, {w, -Pi, Pi}]? –  kguler Jun 17 at 20:48
Or Plot3D[Evaluate[Normal@Series[(Sin [1 + x + y^2])/(4 + x^2 + y^2), {x, 0, 4}, {y, 0, 7}]], {x, -Pi, Pi}, {y, -\[Pi], \[Pi]}, PlotRange -> All] –  Sektor Jun 17 at 20:50

1 Answer 1

Use proper syntax (e.g., Sin[ ] vice Sin( ), Pi vice pi, Normal for Series, Evaluate Plot function to keep from recalculating series expansion for each point).

    Sin[1 + x + y^2]/(4 + x^2 + y^2),
    {x, 0, 4}, {y, 0, 7}] //
 {x, -Pi, Pi}, {y, -Pi, Pi},
 ClippingStyle -> None]

enter image description here

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This is exactly what I needed. Thank you so much. –  Mary Jun 17 at 21:49

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