Why is Plot within Manipulate not evaluating here?

Question

I'm trying to get Plot within my Manipulate to evaluate, but I keep getting error messages:

F[x_]:= Cos[x]

Manipulate[
    Plot[
        Sum[
            ( ( D[ F[x], {x, k} ] /. x -> (π/6) )/k! ) * (x - (π/6) )^k ,
            {k, 1, terms}
        ], 
        {x, -3 π, 3 π}
    ], 
    {terms, 1, 100, 1}
]

It's supposed to be a taylor series that I can manipulate. Help is appreciated!

Edit: I'm very new to Mathematica, so I would appreciate, if you explained everything in a very simplified manner!

Try giving the variable with respect to which you're differentiating a different name than the plotting variable. E.g., Manipulate[ Plot[Sum[((D[F[xx], {xx, k}] /. xx -> (\[Pi]/6))/k!)*(x - (\[Pi]/6))^ k, {k, 1, terms}], {x, -3 \[Pi], 3 \[Pi]}], {terms, 1, 100, 1}] — jjc385, Apr 13 '17 at 03:25
Or, calculate the function before it is supplied to Plot, e.g. With[{fcn = Sum[((D[F[x], {x, k}] /. x -> (\[Pi]/6))/k!)*(x - (\[Pi]/6))^k, {k,1, terms}]}, Plot[fcn, {x, -3 \[Pi], 3 \[Pi]}] ]. — rcollyer, Apr 13 '17 at 03:26
Possible duplicate: https://mathematica.stackexchange.com/questions/1301/generalivar-is-not-a-valid-variable-when-plotting-what-actually-causes-this — Michael E2, Apr 13 '17 at 15:28

ubpdqn · Accepted Answer · 2017-04-13T03:45:58.103

2

Correction

As pointed out by J.M. needs k=0 term to be correct: You can define the sum as function (and change differential variable),e.g.:

sum[x_, n_] := 
 Sum[((D[F[u], {u, k}] /. u -> (\[Pi]/6))/k!)*(x - (\[Pi]/6))^k, {k, 
   0, n}]
Manipulate[Plot[sum[x, n], {x, -3 Pi, 3 Pi}], {n, Range[0,100]}]

This image shows manipulate works for original answer (without constant):

edited Apr 13 '17 at 03:45

answered Apr 13 '17 at 03:33

ubpdqn

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Thank you so so much this was so helpful. Also, just wondering, why wasn't mine working? – Mmnoob Apr 13 '17 at 03:36
@Mmnoob your derivative used the same variable as your function and conflcted. Run the sum outside the Manipulate as you have written and try to evaluate it as your desired x and n. The errors will provide you insight. Good luck:) – ubpdqn Apr 13 '17 at 03:39
You forgot the constant term, too. Sum[(* stuff *), {k, 0, n}]. – J. M.'s missing motivation Apr 13 '17 at 03:40
@J.M. I merely rewrote the OP function changing the variable of differentiation. I did not look at content. I may leave for OP to use as desired but your comment may prompt this revelation. – ubpdqn Apr 13 '17 at 03:41
@ubpdqn Thank you! Just one more question; if I were to implement a range for my "u" value (instead of /.u -> pi/6 I wanted u to range between -2 and 2) how would I alter my function? Much appreciated :) – Mmnoob Apr 13 '17 at 03:44
sum[x_, n_, a_] := Sum[((D[F[u], {u, k}] /. u -> a)/k!)*(x - a)^k, {k, 0, n}] works, of course. @Mm, you might be interested in Series[] and SeriesCoefficient[]. – J. M.'s missing motivation Apr 13 '17 at 03:49
@J.M. of course...blunder after blunder I will delete my comment and leave yours – ubpdqn Apr 13 '17 at 03:50
@Mmnoob see J.M.'s comment above for your question. My original comment forgot to replace so to achieve: $f(x)=\sum\limits_{j=0}^\infty \frac{f^{(j)}(a)}{j!}(x-a)^j$ – ubpdqn Apr 13 '17 at 03:53
@J.M. Thank you! How would you manipulate the a though with the sliders? Would it be just the same? Also when I did the syntax as you showed above my plot went blank. What went wrong? – Mmnoob Apr 13 '17 at 03:53
@Mm, you should try it, you know... ;) Clear everything (Clear["Global`*"]) before you try the new code. – J. M.'s missing motivation Apr 13 '17 at 03:56
@Mmnoob your s is undefined – ubpdqn Apr 13 '17 at 03:59
sum2[x_, n_, s_] := Sum[((D[F[u], {u, k}] /. u -> s)/k!)*(x - s)^k, {k, 0, n}, {s, -1, 1}] Manipulate[ Plot[sum2[x, n, s], {x, -3 [Pi], 3 [Pi]}, PlotRange -> {-5, 5}], {n, 1, 100, 1}, {s, -1, 1, .5}] Now I have an error message @J.M. – Mmnoob Apr 13 '17 at 04:00
Why did you add {s, -1, 1} to your Taylor sum, when that is supposed to be the expansion point? – J. M.'s missing motivation Apr 13 '17 at 04:07
@J.M. Ah that was my bad! I removed it, and now my code works! I'm going to try it with Series[ ] now! Thank you so much for the help! – Mmnoob Apr 13 '17 at 04:12

Why is Plot within Manipulate not evaluating here?

1 Answers1