Question

函数性质探讨f(x)=sin^2(m/100)x,x属于[0,pi],m=403(用Matlab)

Answer 1

%f(x)=sin^2(m/100)x,x属于[0,pi],m=403

%(1)-----------------

x=0:0.01:pi;

m=403;

f = sin(m*x/100).^2;

plot(x,f);

%(2)---------------

n=100;

x1 = 0:pi/n:pi;

x1 = x1 + pi/2*n;

x1 = x1(1:n-1);

f1 = sin(m*x/100).^2;

n=200;

x2 = 0:pi/n:pi;

x2 = x2 + pi/2*n;

x2 = x2(1:n-1);

f2 = sin(m*x/100).^2;

n=1000;

x3 = 0:pi/n:pi;

x3 = x3 + pi/2*n;

x3 = x3(1:n-1);

f3 = sin(m*x/100).^2;

%(3)--------------------------

m1 = (99*mean(f1)+199*mean(f2)+999*mean(f3))/(99+199+999);

disp('由2产生的函数值的平均值')

disp(m1)

%(4)-----------------------

xx = fsolve(@(x) sin(m*x/100)^2-m1,0.1);

disp('对于x解方程f(x)=均值')

disp(xx)