Math131 Calculus I Newton’s Method Notes 4.8
I. Finding
Roots of Equations
How could you find the exact solutions (roots) of :
(a) 2x + 1 = 5?
(b) 
(c) 
(d) 
Better yet…how would we find the exact roots of these:
(e) 
(f) 
y = f(x)
II. Newton’s Method
r
Formula
for
Math131 Calculus I Notes
4.8 page
2
ex #1 Starting with 
, find the third approximation 
to the root of the equation 
.
ex#2 Use Newton’s Method to find 
correct to eight decimal places.
Math131 Calculus I Notes
4.8 page
3
ex #3 Use the third approximation
of the root of 
using
Give your answer to four decimal places.