0
$\begingroup$

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!

$\endgroup$
4
  • 1
    $\begingroup$ 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}] $\endgroup$
    – jjc385
    Apr 13, 2017 at 3:25
  • $\begingroup$ 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]}] ]. $\endgroup$
    – rcollyer
    Apr 13, 2017 at 3:26
  • 1
    $\begingroup$ 1. You forgot the constant term. 2. Add Evaluate[]: Manipulate[Plot[Evaluate @ Sum[(* stuff *)], (* stuff *)], (* stuff *)] $\endgroup$ Apr 13, 2017 at 3:26
  • $\begingroup$ Possible duplicate: mathematica.stackexchange.com/questions/1301/… $\endgroup$
    – Michael E2
    Apr 13, 2017 at 15:28

1 Answer 1

2
$\begingroup$

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): enter image description here

$\endgroup$
14
  • $\begingroup$ Thank you so so much this was so helpful. Also, just wondering, why wasn't mine working? $\endgroup$
    – Mmnoob
    Apr 13, 2017 at 3:36
  • $\begingroup$ @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:) $\endgroup$
    – ubpdqn
    Apr 13, 2017 at 3:39
  • $\begingroup$ You forgot the constant term, too. Sum[(* stuff *), {k, 0, n}]. $\endgroup$ Apr 13, 2017 at 3:40
  • $\begingroup$ @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. $\endgroup$
    – ubpdqn
    Apr 13, 2017 at 3:41
  • $\begingroup$ @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 :) $\endgroup$
    – Mmnoob
    Apr 13, 2017 at 3:44

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.