Successive approximations
posted by Devin on .
Find all root of ln(4x^2)=x correct to 8 decimal places. List all successive approximations.

by definition:
4  x^2 = e^x
by making a rough sketch of
y = 4x^2 and y = e^x, I can see that there are roots at appr. 1 and 2
setting up for Newton's Method:
let y = 4  x^2  e^x
y' = 2x  e^x
His method says:
newx = x  y/y' = x  (4x^2  e^x)/(2x  e^x)
= x + (4x^2  e^x)/(2x+e^x)
so start with x = 1
newx  x
????  1
1.059707788 1.059707788
1.058007813  1.058007813
1.058006401  1.058006401
1.058006401 YEahhhhh! correct to 9 decimal places
start with x = 2
 1.9649813...
1.964635631  1.964635631
1.964635597  1.964635597
1.964635597 Yeah again,
x = 1.058006401 or x = 1.964635597