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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.

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  • $\begingroup$ That's just the derivative you want; try f'[1.5]. $\endgroup$ – J. M. will be back soon May 31 '13 at 1:58
  • $\begingroup$ 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'. $\endgroup$ – Mark McClure May 31 '13 at 2:04
  • $\begingroup$ I know it's the derivative. I want my students to find a derivative with a limit. $\endgroup$ – user7716 May 31 '13 at 2:16
  • $\begingroup$ In general, interpolated functions seem fussy compared to user defined functions. $\endgroup$ – user7716 May 31 '13 at 2:16
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    $\begingroup$ 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. $\endgroup$ – Daniel Lichtblau May 31 '13 at 3:12
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Try:

<< NumericalCalculus`
f = Interpolation[Table[{x, x  x}, {x, 1, 5}]];
NLimit[(f[3 + h] - f[3])/h, h -> 0]
(*
 6
*)
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  • $\begingroup$ 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. $\endgroup$ – user7716 May 31 '13 at 2:48
  • $\begingroup$ I still get errors, but I am at least getting an answer along with the errors now. Thank you! $\endgroup$ – user7716 May 31 '13 at 2:53
  • $\begingroup$ 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 $\endgroup$ – user7716 May 31 '13 at 2:56
  • $\begingroup$ @user, because NLimit[] is not built-in, and it is in the NumericalCalculus` package which needs to be explicitly loaded... $\endgroup$ – J. M. will be back soon May 31 '13 at 4:30

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