Posted by Devin on Saturday, October 20, 2012 at 9:00pm.
Find all root of ln(4x^2)=x correct to 8 decimal places. List all successive approximations.

Successive approximations  Reiny, Thursday, April 4, 2013 at 12:35am
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
Answer This Question
Related Questions
 math  Find all roots of the equation ln(4x^2)=x correct to 8 decimal places. ...
 CALCULUS  Use Newton's method to find all the roots of the equation correct to ...
 Math  Locate the square root of negative 15 and the square root of 94 cubed to ...
 Precalculus  Suppose 3 mg of a drug is injected into a person's bloodstream. As...
 calculus  Use the Newton method to approximate the indicated zero of the ...
 Calculus  Starting with an initial guess of x=2, use Newtonâ€™s method to ...
 Chem  What simplifying assumptions do we usually make in working problems ...
 Math  please help!!!!Apply newtons method to approximate the xvalues of the ...
 Calculus  please help!!!!Apply newtons method to approximate the xvalues of ...
 Corporate Finance  An investment today of $3,3OO is worth $10,000 IN 8 YEARS. ...
More Related Questions