Question

For the function f(x) = e^(x/2) + 2*x -0.3 Range -2 <xs2 a) Write a Matlab program to find the numerical solution of f(x) using the Bisection Method. Important Note: i. Include a copy of your Matlab code in your solution.

Answer 1

Code to copy along with screenshots of code and output are provided.

Make sure to save the code into a matlab script file before executing it.
Please refer to screenshots to understand the indentation of code.
If you have any doubts or issues. Feel free to ask in comments
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Screenshots of Code :

test.m X + 1 $ to clear the screen clc; 2 - 3 4 $declaring function handle funct = @(x) exp (x/2) + 2*x -0.3; 5 - 6 7 8 $ declaring upper and lower limits upper = 2; lower = -2; 9 10 11 12 13 14 - 15 16 17 - 18 _ #looping for 100 times Çfor i = 1:100 calculating mid value (bisection) mid = (lower + upper)/2; $ if negative means that values doesnt exist between mid and uppper so, & make lower = mid if funct (mid)* funct (x_upper) < 0 lower = mid; $ if positive means that values exist in this interval and make $ upper = mid else upper = mid; end $ if value is close to 0.001 then break the loop if abs (funct (upper)) <0.001 break; 19 20 21 - 22 - - 23 24 25 26 -

27 end end 28 29 30 31 32 - 33 $ printing answer fprintf(" Answer = $f \n', upper); 34 35

Screenshots of Output :

Answer -0.283691

Code to copy:

% to clear the screen
clc;

%declaring function handle
funct = @(x) exp(x/2) + 2*x -0.3;

% declaring upper and lower limits
upper = 2;
lower = -2;

% looping for 100 times
for i = 1:100
% calculating mid value (bisection)
mid = (lower + upper)/2;
% if negative means that values doesnt exist between mid and uppper so,
% make lower = mid
if funct(mid)* funct(x_upper) < 0
lower = mid;
% if positive means that values exist in this interval and make
% upper = mid
else
upper = mid;
end
% if value is close to 0.001 then break the loop
if abs(funct(upper))<0.001
break;
end

end

% printing answer
fprintf(' Answer = %f \n ', upper);

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Plot for reference (not asked in question , just for understanding that function becomes 0 near x = -0.28):

8 6 2 0 -2 -4 -2 -1.5 -1 -0.5 0 0.5 1 1.5 N

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