Roots of equations                      interval
(a) f(x) = exp(x)*ln(x) - cos(x*2) = 0  [1.0, 4.0]
(b) f(x) = ln(x2+2)*cos(x)+sin(x) = 0   [0.0, 4.0]
(c) f(x) = exp(x) - sin(pi*x/3) = 0     [-5.0,2.0]
(d) f(x) = x2 - 6x +9 = 0               [-5.0, 5.0]

 Solutions (tolerance eps = 1.0e-6)

             CLOSED DOMAIN METHODS
     Bisection method     False position method
      iter.   root        iter.  root
a)     22    1.11303       62    1.11302
b)     22    2.06917        7    2.06917
c)     23   -3.04545        9   -3.04545
d)          no roots            no roots


               OPEN DOMAIN METHODS
      Secant method          Newton method
      xi   iter.   root      xi   iter.  root
a)    1.0   5    1.11303     1.0   4    1.11302
b)    0.0   5   -0.75726     0.0   4   -0.75726
      1.5   6    2.06917     1.5   5    2.06917
c)   -5.0   6   -5.99763    -5.0   5   -5.99763
     -4.0   6   -3.04545    -4.0   5   -3.04545
d)   -5.0  32    3.00000    -5.0  14    2.99999


Multiple roots of equation
(e) f(x) = ln(x^2+2)*cos(x)+sin(x) = 0     [-10.0, 10.0]
(f) f(x) = x^3 - 5x^2 + 7x - 3 = 0         [-10.0, 10.0]
(g) f(x) = sin(x^2)*cos(x+1)/(x^2+1) = 0   [  1.0,  6.0]

brute force method together with the bisection method

      (e)                   (f)                  (g)
 root      value       root      value      root      value
    1    -7.61441        1     1.00000         1     1.77245
    2    -4.39654        2     1.00000         2     2.50663
    3    -0.75726        3     3.00000         3     3.06998
    4     2.06917                              4     3.54491
    5     5.00676                              5     3.71239
    6     8.08715                              6     3.96333
                                               7     4.34161
                                               8     4.68947
                                               9     5.01326
                                              10     5.31736
                                              11     5.60499
                                              12     5.87856