Sunday

March 29, 2015

March 29, 2015

Posted by **Devin** on Saturday, October 20, 2012 at 9:00pm.

- Successive approximations -
**Reiny**, Thursday, April 4, 2013 at 12:35amby 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

**Answer this Question**

**Related Questions**

math - Find all roots of the equation ln(4-x^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 ...

Chem - What simplifying assumptions do we usually make in working problems ...

Math - please help!!!!Apply newtons method to approximate the x-values of the ...

Calculus - please help!!!!Apply newtons method to approximate the x-values of ...

Corporate Finance - An investment today of $3,3OO is worth $10,000 IN 8 YEARS. ...

Calculus - Use Newton's Method to approximate the positive root of the function ...