Posted by **lucy** on Wednesday, April 3, 2013 at 10:28pm.

Find all roots of the equation ln(4-x^2)=x correct to 8 decimal places. List all successive approximations.

- math -
**Reiny**, Thursday, April 4, 2013 at 12:41am
by definition:

4 - x^2 = e^x

by making a rough sketch of

y = 4-x^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 - (4-x^2 - e^x)/(-2x - e^x)

= x + (4-x^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

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