write a script that displays in a single figure window a plot of the functions x, x^2,x^3,x^4, and x^5 across the interval [0, 1]. in matlab

To plot the functions x, x^2, x^3, x^4, and x^5 across the interval [0, 1] in MATLAB, you can follow the steps below:

1. Create a vector x with values from 0 to 1 using the linspace function:

main.m
x = linspace(0, 1);
20 chars
2 lines

2. Calculate the functions y1 = x, y2 = x.^2, y3 = x.^3, y4 = x.^4, and y5 = x.^5:

main.m
y1 = x;
y2 = x.^2;
y3 = x.^3;
y4 = x.^4;
y5 = x.^5;
52 chars
6 lines

3. Open a figure window using the figure function:

main.m
figure;
8 chars
2 lines

4. Plot the functions using the plot function:

main.m
plot(x, y1, x, y2, x, y3, x, y4, x, y5);
41 chars
2 lines

5. Add a legend to the plot using the legend function:

main.m
legend('x', 'x^2', 'x^3', 'x^4', 'x^5');
41 chars
2 lines

6. Add labels to the x-axis and y-axis using the xlabel and ylabel functions:

main.m
xlabel('x');
ylabel('y');
26 chars
3 lines

7. Add a title to the plot using the title function:

main.m
title('Plot of x, x^2, x^3, x^4, and x^5');
44 chars
2 lines

Putting it all together, here's the complete MATLAB script:

main.m
x = linspace(0, 1);
y1 = x;
y2 = x.^2;
y3 = x.^3;
y4 = x.^4;
y5 = x.^5;
figure;
plot(x, y1, x, y2, x, y3, x, y4, x, y5);
legend('x', 'x^2', 'x^3', 'x^4', 'x^5');
xlabel('x');
ylabel('y');
title('Plot of x, x^2, x^3, x^4, and x^5');
232 chars
13 lines

Running this script will display a single figure window with the plot of the functions x, x^2, x^3, x^4, and x^5 across the interval [0, 1].

Note: The ^ operator is used for element-wise exponentiation in MATLAB.