import numpy as np
import matplotlib.pyplot as plt
from math import cos,sin,fabs

def f(x):
    return sin(x)

def df(x):
    return cos(x)

def dfh(f,x,h):
    return (f(x+h)-f(x)) / h


n = 100
h_vec = 10.0**np.linspace(-14, -3, n)
error_vec = np.zeros((n,1))
x = 1

for i in range(n):
    error_vec[i] = fabs(dfh(f,x,h_vec[i]) - df(x))

    
plt.loglog(h_vec, np.asarray(error_vec),'*-',label='sin(x), x=1')
plt.xlabel('h')
plt.ylabel('feil i numerisk derivert')
plt.legend()
plt.savefig('numdiff.pdf')
plt.show()