meyers hw 4.ipynb

Kernel: SageMath 8.2

#pg 59: 1,3,7

import numpy as np
import scipy.optimize as sci

x0 = 0

def f1a(x):
    return x**3-2*x+2
def f1b(x):
    return np.exp(x)-7
def f1c(x):
    return np.exp(x)+np.sin(x)-4+x


# My implementation ran into overflow errors
# def noot(fx,x0=x0, maxiter=200):
#     xs = [x0]
#     i = 0
#     while (i < maxiter):
#         fx0 = (fx(xs[i]))
#         dfx0 = derivative(fx,x)(xs[i])
#         xs.append(x0-(fx0/dfx0))
#         i = i +1
#         print(xs[i])
#     return xs[i]
# # print('1(a) = ',noot(f1a,x0))
# # print('1(b) = ',noot(f1b,x0))
# # print('1(c) = ',noot(f1c,x0))

print(sci.newton(f1a, x0, fprime=None, args=(), tol=1.48e-08, maxiter=50, fprime2=None))
print(sci.newton(f1b, x0, fprime=None, args=(), tol=1.48e-08, maxiter=50, fprime2=None))
print(sci.newton(f1c, x0, fprime=None, args=(), tol=1.48e-08, maxiter=50, fprime2=None))


# noot(f1a)
# noot(f1b)
# noot(f1c)

-1.76929235424
1.94591014906
0.864726265677

#and so on and so on