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import math
 
 
def f(x):
    return x**3 - 3
 
 
def df(x):
    return 3 * x**2
 
 
def g(x):
    return 5*x + math.log(x, math.e) - 10000
 
 
def dg(x):
    return 5 + 1/x
 
 
def h(x):
    return 2 - x**2 - math.sin(x)
 
 
def dh(x):
    return -2*x - math.cos(x)
 
 
def j(x):
    return x**2 - 10
 
 
def dj(x):
    return 2*x
 
 
def k(x):
    return math.log((x**2 + 1), math.e) - math.e**(0.4*x)*math.cos(math.pi * x)
 
 
def dk(x):
    return math.pi * math.e**((2 * x) / 5) * math.sin(math.pi * x) - (((2 * math.e**((2 * x) / 5)) * math.cos(math.pi * x)) / 5) + ((2 * x) / (x**2 + 1))
 
 
def calc_relative_error(current_error, last_error):
    return abs((current_error - last_error) / current_error)
 
 
def functions(function_name, x):
    if function_name == "f":
        return f(x)
    if function_name == "df":
        return df(x)
    if function_name == "g":
        return g(x)
    if function_name == "dg":
        return dg(x)
    if function_name == "h":
        return h(x)
    if function_name == "dh":
        return dh(x)
    if function_name == "j":
        return j(x)
    if function_name == "dj":
        return dj(x)
    if function_name == "k":
        return k(x)
    if function_name == "dk":
        return dk(x)
 
 
def newton_rhapson(x, n, tol, function_name, derivative):
    for i in range(n):
        if functions(function_name, x) == 0:
            return x
        if functions(derivative, x) == 0:
            break
 
        last_estimate = x
        x = x - (functions(function_name, x) / functions(derivative, x))
        current_estimate = x
        relative_error = calc_relative_error(current_estimate, last_estimate)
 
        if relative_error <= tol:
            return current_estimate
    return -1
 
 
# Function specific variables
f_start = 2.5
g_start = 3
h_start = -2
h2_start = 3
j_start = 3
k_start = -2
 
root_f = newton_rhapson(f_start, 10, 1.E-1, "f", "df")
root_g = newton_rhapson(g_start, 100, 1.E-9, "g", "dg")
root_h = newton_rhapson(h_start, 100, 1.E-9, "h", "dh")
root_h2 = newton_rhapson(h2_start, 100, 1.E-9, "h", "dh")
root_j = newton_rhapson(j_start, 100, 1.E-9, "j", "dj")
root_k = newton_rhapson(k_start, 100, 1.E-9, "k", "dk")
 
print(root_f)
print(root_g)
print(root_h)
print(root_h2)
print(root_j)
print(root_k)