matlab code Write the function find_zero that is defined like this function x =

Question

matlab code

Write the function find_zero that is defined like this function x = find_zero(f,x1,x2). The first input argument is special. It is a “function handle”. A function handle is gotten by typing   @ and   the   name   of   any   function.   For   example, x = find_zero(@sin,-1,1) will give f the function    handle    for    MATLAB’s    built-in    sin function. Then, inside find_zero, the statement y = f(-1) would set y = sin(-1). Note that the @ sign is not used inside the function. Only the caller uses it. All other arguments to find_zero are scalar numbers, and x1 is less than x2. The goal of the function is to find an x that lies in the range from x1 to x2 such that after the command, y = f(x), is executed inside the function find_zero, y is approximately zero as defined by abs(y) < 1e-10. All you know about the function f is that it has one scalar input and one scalar output, and a plot of its values crosses the x-axis exactly once between x1 and x2, as, for example, in the figure 3. It is the responsibility of the caller to call the function with arguments that obey these rules.

Figure 3 Output plot for x1 and x2 (Hint: Remember to label your axis’s)

Here are two sample runs:

>> find_zero(@sin,-2.5,2.3) % as shown in the figure

ans =

-6.4000e-11

>> format long

>> find_zero(@cos,-2,1.3)

ans =

-1.570796326871000

note: i have to get same answer without any errors or warnings and thank you

Explanation / Answer

function mid = find_zero(fun, x1, x2)
    if fun(x1) * fun(x2) > 0
        return; %probably no solution
    end
  
    if fun(x1) < 0 %we expect fun(x1) > 0 and fun(x2) < 0
        t = x1;
        x1 = x2;
        x2 = t;
    end
  
    mid = (x1 + x2)/2; %find the mid mpoint and value at mid point
    y = fun(mid);
  
    while abs(y) >= 1e-10 %while more than threshold
        if y > 0 %replace x1 if mid produces +ve value
            x1 = mid;
        else %replace x2
            x2 = mid;
        end
        mid = (x1 + x2)/2;
        y = fun(mid);
    end
end

I hope this answer helps you. I tried my best to keep the answer as simple as possible. If you need any assistance on this please let me know. I shall try my best to resolve all your issue!

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