Answer:
The root is:

Explanation:
Use this script in Matlab:
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function  [c, err, yc] = bisect (f, a, b, delta)
% f the function introduce as n anonymous function
%       - a y b are the initial and the final value respectively
%       - delta is the tolerance or error.
%           - c is the root
%       - yc = f(c)
%        - err is the stimated error for  c
ya = feval(f, a);
yb = feval(f, b);
if  ya*yb > 0, return, end
max1 = 1 + round((log(b-a) - log(delta)) / log(2));
for  k = 1:max1
 c = (a + b) / 2;
 yc = feval(f, c);
 if  yc == 0
  a = c;
  b = c;
 elseif  yb*yc > 0
  b = c;
  yb = yc;
 else
  a = c;
  ya = yc;
 end
 if  b-a < delta, break, end
end
c = (a + b) / 2;
err = abs(b - a);
yc = feval(f, c);
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Enter the function in matlab like this:
f= @(x) 0.005*(exp(2*x)*cos(x))
You should get this result:
f =
  function_handle with value:
    @(x)0.005*(exp(2*x)*cos(x))
Now run the code like this:
[c, err, yc] = bisect (f, 1, 2, 1e-10)
You should get this result:
c =
    1.5708
err =
   5.8208e-11
yc =
  -3.0708e-12
In addition, you can use the plot function to verify your results:
fplot(f,[1,2])
grid on