Question

The given equation has a root in the indicated interval.In MatLab, use the Bisection method to generate the first four midpoints and intervals (besides the original interval given) containing the root.

equation: e^x - 2x= 2,[0,2]

Answer 1

--------------------------------------------------------------------------------------------------------------------------------

code

-------------------------------------------------------------------------------------------------------------------------

clear all;

f=@(x) exp(x)-2*x-2;      
a=0;
b=2;

fprintf('Given Interval %f %f\n',a,b);

j=0;

for i=1:4
c=(a+b)/2;
fprintf('For Interval-%d %f %f Mid Point is %f \n',j,a,b,c);
j=j+1;
if f(c)>0
   b=c;
else a=c;
end
end


fprintf('Root of given equation is %f',c)

----------------------------------------------------------------------------

Output

------------------------------------------------------------------------------------------

Given Interval 0.000000 2.000000
For Interval-0 0.000000 2.000000 Mid Point is 1.000000
For Interval-1 1.000000 2.000000 Mid Point is 1.500000
For Interval-2 1.500000 2.000000 Mid Point is 1.750000
For Interval-3 1.500000 1.750000 Mid Point is 1.625000
Root of given equation is 1.625000>>