Patterns in error terms while approximating a function with its Taylor/McLauren expansion

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If you find the area difference between a function and its Taylor or McLauren expansion ( the bounds of the integral being where the expanson is valid ) for each ongoing term, does some type of series form between the area differences from each ongoing term of the expansion?



One would expect that the area difference between the function and its approximate would decrease with each ongoing term of the expansion, but is there a common factor so that the errors form a geometric progression? or does it depend on said function?




calculus sequences-and-series approximation




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  • It might help if you showed an example of what you mean, but the answer is likely to be your "does it depend on said function?"
    – Henry
    Aug 26 at 10:27










  • The "area difference" would be the integral of the "remainder" of the Taylor approximation, would it not? The remainder certainly depends upon the function, but there are things one can say about it.
    – Blue
    Aug 26 at 13:10














up vote
1
down vote

favorite
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If you find the area difference between a function and its Taylor or McLauren expansion ( the bounds of the integral being where the expanson is valid ) for each ongoing term, does some type of series form between the area differences from each ongoing term of the expansion?



One would expect that the area difference between the function and its approximate would decrease with each ongoing term of the expansion, but is there a common factor so that the errors form a geometric progression? or does it depend on said function?




calculus sequences-and-series approximation




share|cite|improve this question






















  • It might help if you showed an example of what you mean, but the answer is likely to be your "does it depend on said function?"
    – Henry
    Aug 26 at 10:27










  • The "area difference" would be the integral of the "remainder" of the Taylor approximation, would it not? The remainder certainly depends upon the function, but there are things one can say about it.
    – Blue
    Aug 26 at 13:10












up vote
1
down vote

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up vote
1
down vote

favorite
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If you find the area difference between a function and its Taylor or McLauren expansion ( the bounds of the integral being where the expanson is valid ) for each ongoing term, does some type of series form between the area differences from each ongoing term of the expansion?



One would expect that the area difference between the function and its approximate would decrease with each ongoing term of the expansion, but is there a common factor so that the errors form a geometric progression? or does it depend on said function?




calculus sequences-and-series approximation




share|cite|improve this question














If you find the area difference between a function and its Taylor or McLauren expansion ( the bounds of the integral being where the expanson is valid ) for each ongoing term, does some type of series form between the area differences from each ongoing term of the expansion?



One would expect that the area difference between the function and its approximate would decrease with each ongoing term of the expansion, but is there a common factor so that the errors form a geometric progression? or does it depend on said function?





calculus sequences-and-series approximation





share|cite|improve this question













share|cite|improve this question




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edited Aug 31 at 10:34









DevashishKaushik

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asked Aug 26 at 10:18









Tan Sriprai

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  • It might help if you showed an example of what you mean, but the answer is likely to be your "does it depend on said function?"
    – Henry
    Aug 26 at 10:27










  • The "area difference" would be the integral of the "remainder" of the Taylor approximation, would it not? The remainder certainly depends upon the function, but there are things one can say about it.
    – Blue
    Aug 26 at 13:10
















  • It might help if you showed an example of what you mean, but the answer is likely to be your "does it depend on said function?"
    – Henry
    Aug 26 at 10:27










  • The "area difference" would be the integral of the "remainder" of the Taylor approximation, would it not? The remainder certainly depends upon the function, but there are things one can say about it.
    – Blue
    Aug 26 at 13:10















It might help if you showed an example of what you mean, but the answer is likely to be your "does it depend on said function?"
– Henry
Aug 26 at 10:27




It might help if you showed an example of what you mean, but the answer is likely to be your "does it depend on said function?"
– Henry
Aug 26 at 10:27












The "area difference" would be the integral of the "remainder" of the Taylor approximation, would it not? The remainder certainly depends upon the function, but there are things one can say about it.
– Blue
Aug 26 at 13:10




The "area difference" would be the integral of the "remainder" of the Taylor approximation, would it not? The remainder certainly depends upon the function, but there are things one can say about it.
– Blue
Aug 26 at 13:10















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