please show all matlab code involved: Use matlab to plot the functions e^(x/5) a

Question

please show all matlab code involved:

Use matlab to plot the functions e^(x/5) and sin(x). Make approximations to the points where they are equal.

[Midpoint Method] Write a short matlab program which will implement the midpoint method, given initial intervals [ak,bk]. Use the results from the above step to implement the program, and nd the approximations to the points where f(x) = e^(x/5) sin(x) = 0. Let the midpoint method run until f(x) < 107. Count the number of steps that the midpoint method takes for each point.

Explanation / Answer

matlabfun.m

clc
clear all
close all

%% Part a
f1 = @(x) exp(-x/5);
f2 = @(x) sin(x);
fplot(f1,[0 1])
hold on
fplot(f2,[0 1])
hold off;

%% Part b
f = @(x) exp(-x/5) - sin(x);
it = 0;
a = 0;
b = 1;
cond = 1;

while (cond > 0)
    it = it + 1;
    c = (a+b)/2 ;
    if (f(c) < 10^-7)
        cond = 0;
    else
        if (f(a) > 0) && (f(b) < 0)
            if f(c) > 0
                a = c;
            else
                b = c;
            end
        elseif (f(a) < 0) && (f(b) > 0)
            if f(c) > 0
                b = c;
            else
                a = c;
            end
        end
    end
end

it
              

Output :

it =

     5

at approximate x = 0.958 and y = 0.818 both function are equal

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