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I have an interpolated function

f = Interpolation[data]

I would like to calculate limits such as

Limit[(f[1.5 + h] - f[1.5])/h, h -> 0]

I just get errors.

share|improve this question
That's just the derivative you want; try f'[1.5]. – J. M. May 31 '13 at 1:58
Limit is a purely algebraic tool. You could try NLimit from the NumericalCalculus package. I concur with J.M., however, that your specific example would be best approached with f'. – Mark McClure May 31 '13 at 2:04
I know it's the derivative. I want my students to find a derivative with a limit. – user7716 May 31 '13 at 2:16
In general, interpolated functions seem fussy compared to user defined functions. – user7716 May 31 '13 at 2:16
While I agree it might be a reasonable thing to do, at this time Limit is not going inside the InterpolatingFunction to extract a local interpolant polynomial. – Daniel Lichtblau May 31 '13 at 3:12
up vote 0 down vote accepted


<< NumericalCalculus`
f = Interpolation[Table[{x, x  x}, {x, 1, 5}]];
NLimit[(f[3 + h] - f[3])/h, h -> 0]
share|improve this answer
Thanks, this is not working for me. I am not sure how to copy and paste my code into a comment to show you. I am trying to figure it out. – user7716 May 31 '13 at 2:48
I still get errors, but I am at least getting an answer along with the errors now. Thank you! – user7716 May 31 '13 at 2:53
Can you explain why I needed the <<NumericalCalculus`? Isn't NLimit already defined without any special packages? That line is what seems to make the difference – user7716 May 31 '13 at 2:56
@user, because NLimit[] is not built-in, and it is in the NumericalCalculus` package which needs to be explicitly loaded... – J. M. May 31 '13 at 4:30

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