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

ID: 3837683 • Letter: M

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

0.5 0.5 x1 x2

Explanation / Answer

>> 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

in the function:

>> function x = find_zero(f,x1,x2) % Function definition

>> y = f(x2); % Computing the function value at x = x2

>> while abs(y) > 1e-10 % exit loop if y approximatly equal to zero

     >> x=x2-y*(x2-x1)/(y-f(x1)); % finding new x using secant method

    >> x1=x2;%copy the value of x2 to x1

    >> x2=x;% copy the value of x to x2

     >> y = f(x2); % Computing the function value at new x

>> end % End of loop

>> end % End of program