CoCalc Public FilesNewton's method to approximate cube root of 4.ipynb
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Compute Environment: Ubuntu 20.04 (Default)

This activity asks to use three iterations of Newton's method to approximate the cube root of 4.First I define a function calls newton and that function I have "f" which is the original function, "df" as the derivation of the original function, x represents the initial value, n stands for the number of iterations,and err is the error which I use the value of 0.0001.So since the function is given and I have the error value, I will need to find the x value in order to find the approximate value for the cube root of 4.So I graph my original function in Desmos and I find that the root is actually between 1 and 2 then I pick 1 as for my x value. After plotting everything I found out with three iteration of Newton's method to approximate the cube root of 4 with an error of 0.0001 is 2.

In [ ]:


In [1]:
def newton(f, df,x,n,err):
i=0
while abs(f(x))> err and i<=n:
x= x-f(x)/df(x)
i +=1
if n>n:
return false
else:
return x

In [2]:
def myf(x):
return x**3-4

def myfderiv(x):
return 3*x**2

In [1]:
newton(myf,myfderiv,1.5,3,0.0001)

--------------------------------------------------------------------------- NameError Traceback (most recent call last) <ipython-input-1-933d163d298d> in <module> ----> 1 newton(myf,myfderiv,1.5,3,0.0001) NameError: name 'newton' is not defined