CoCalc Public FilesNewtons Method for Cube Root.ipynbOpen with one click!
Author: Julia Burnside
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Compute Environment: Ubuntu 20.04 (Default)

Newton's Method to approximate cube roots

Approximating 43\sqrt[3]{4}

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def newton(c, dc, x, n, err): i=0 while abs(c(x)) > err and i <=n: x=x-c(x)/dc(x) i+=1 if i > n: return False else: return x def cubic(x): return x**3-4 def cubicDerivative(x): return 3*x**2 print("cube root of 4 = 4^(1/3) =", 4**(1/3), '\n') print("Using Newton's Method:", '\n') print("1st guess = 1:", '\n', newton(cubic, cubicDerivative, 1, 4, 0.0001), '\n') print("2nd guess = 1.5:", '\n', newton(cubic, cubicDerivative, 1.4, 5, 0.0001),'\n') print("3rd guess = 1.5 (decreasing err to 0.0000000001):", '\n', newton(cubic, cubicDerivative, 1.5, 4, 0.0000000001),"<-- this is the most accurate")
cube root of 4 = 4^(1/3) = 1.5874010519681994 Using Newton's Method: 1st guess = 1: 1.5874096961416333 2nd guess = 1.5: 1.587401164777749 3rd guess = 1.5 (decreasing err to 0.0000000001): 1.5874010519681996 <-- this is the most accurate
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