- #1
NYK
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- 0
I have been working on writing g a script file that will:
I pasted the script I have so far bellow:
clear, clc, close all
%Define the limits, the original function and the Taylor series.
syms x
a = -2*pi:2*pi;
g = (5*sin(3*x));
T_2 = taylor(g, 'Order', 2);
T_5 = taylor(g, 'Order', 5);
T_50 = taylor(g, 'Order', 50);
z = (5*sin(3*a));%plot the original function and the three Taylor series.
fg=figure;
ax=axes;
ez1=plot(a,z, 'r--');
hold on
ez2=ezplot(char(T_2),[-2*pi, 2*pi]);
ez3=ezplot(char(T_5),[-2*pi, 2*pi]);
ez4=ezplot(char(T_50),[-2*pi, 2*pi]);
legend('5sin(3x)','T2','T5','T50')
set(ez2, 'color', [0 1 0])
set(ez3, 'color', [0 0 1])
set(ez4, 'color', [1 0 1])title(ax,['Graph of 5sin(3x) and taylor expansions T2, T5 and T50'])
- Calculate f(x)=5sin(3x) using the Taylor series with the number of terms n=2, 5, 50, without using the built-in sum function.
- Plot the three approximations along with the exact function for x=[-2π 2π].
- Plot the relative true error for each of the approximations
- Calculate the value of sin(x) and the error for x=π and x=3π/2 for each of the approximations
- How many terms are necessary for an error E<.000001?
I pasted the script I have so far bellow:
clear, clc, close all
%Define the limits, the original function and the Taylor series.
syms x
a = -2*pi:2*pi;
g = (5*sin(3*x));
T_2 = taylor(g, 'Order', 2);
T_5 = taylor(g, 'Order', 5);
T_50 = taylor(g, 'Order', 50);
z = (5*sin(3*a));%plot the original function and the three Taylor series.
fg=figure;
ax=axes;
ez1=plot(a,z, 'r--');
hold on
ez2=ezplot(char(T_2),[-2*pi, 2*pi]);
ez3=ezplot(char(T_5),[-2*pi, 2*pi]);
ez4=ezplot(char(T_50),[-2*pi, 2*pi]);
legend('5sin(3x)','T2','T5','T50')
set(ez2, 'color', [0 1 0])
set(ez3, 'color', [0 0 1])
set(ez4, 'color', [1 0 1])title(ax,['Graph of 5sin(3x) and taylor expansions T2, T5 and T50'])