CoCalc -- 11-1-21 Participation.ipynb

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ubuntu2004

Kernel: Python 3 (system-wide)

In [8]:

def bisection(a,b,f,err):
    c = (a+b)/2
    while c - a > err:
        if f(c) == 0:
            return c
        elif f(a)*f(c) > 0:
            a = c
        else:
            b = c
        c = (a+b)/2
    return c

We use the bisection method which has already been written.

In [9]:

import numpy as np
import matplotlib.pyplot as plt

We import these items so that we can produce a graph.

In [10]:

def formula(x):
    return np.log(x) - np.sin(x)

In [11]:

x = np.linspace(2,4,1000)
y = np.log(x) - np.sin(x)
plt.plot(x,y)

Out[11]:

[<matplotlib.lines.Line2D at 0x7f2002d929d0>]

We see in the graph that 2.25 is the closest to zero so we put 2.25 into the bisection formula to see how close it is.

In [13]:

bisection(2,2.25,formula,0.001)

Out[13]:

2.2197265625

In [14]:

formula(2.2197265625)

Out[14]:

0.0006532685362758972

This is basically pretty much zero so this works out.

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