## mukushla 3 years ago write a mfile with matlab which takes a and n from user and gives the n term s of taylor series of sin(x) around x=a

1. mukushla

i have difficulties with math part @experimentX

2. mukushla

we must print something like this$a_0+a_1(x-a)+a_2(x-a)^2+...$

3. mukushla

man i have nothing :(

4. experimentX

Woops ... !! probably write a function do do that.

5. experimentX

syms x diff(sin(x), 'n times differentiate', 'around a');

6. mukushla

@phi

7. mukushla

8. experimentX

Woops!! lol

9. mukushla

lol

10. mukushla

nth derivative of sin(x)$\sin(\frac{n\pi}{2}+x)$

11. mukushla

wrong !!!

12. experimentX

Woops ... i need to differentiate it and substitute it.

13. experimentX

clc syms x center = input('Enter the center of expansion: '); for i=1:10 disp(subs(diff(sin(x), i), x, center)); end

14. mukushla

exper can we show that like what i mentioned above?

15. mukushla

for example with center 3 -0.9900-0.1411(x-3)+0.9900(x-3)^2+...

16. experimentX

hold on ... I'm working.

17. experimentX

I don't like Matlab's string handing !!

18. mukushla

me too

19. phi

This does not do the input. But it does give an idea a=pi/3, n=4; str2=''; for ii=0:(n-1) switch mod(ii,4) case 0, ff= sin(a); case 1, ff= cos(a); case 2, ff= -sin(a); case 3, ff= -cos(a); end; if (ff<0) sg= '-' else sg= '+'; end; if ii>0 str= sprintf('%2s %7.5f(x-%2.4f)^%d',sg, abs(ff)/factorial(ii),a,ii); else str= sprintf('%7.5f',ff); end; str2= [str2 str]; end; str2

20. phi

its output str2 = 0.86603 + 0.50000(x-1.0472)^1 - 0.43301(x-1.0472)^2 - 0.08333(x-1.0472)^3

21. experimentX

I really hate matlab for string manipulation clc syms x center = input('Enter the center of expansion: '); for i=1:3 disp( [subs(diff(sin(x), i), x, center), strcat('(x-', num2str(center), ')^', num2str(i))]); end

22. experimentX

I got this nasty code ... looks pretty close clc syms x center = input('Enter the center of expansion: '); to_out = ''; for i=1:10 to_out = strcat(to_out, '+' , strcat(char(subs(diff(sin(x), i), x, center)), strcat('(x-', num2str(center), ')^', num2str(i)))); end disp(to_out);

23. experimentX

the out put is ...for r=4 ... maybe tweak a little. +cos(3)(x-3)^1+-sin(3)(x-3)^2+-cos(3)(x-3)^3+sin(3)(x-3)^4

24. mukushla

thank u guys

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