Tuesday

September 2, 2014

September 2, 2014

Posted by **Anonymous** on Tuesday, June 1, 2010 at 7:03pm.

e^x - 2. If you first guess is x1=1, what value will you calculate for the next approximation x2?

...I don't know what Newton's method is, so I looked it up...and I'm still confused. Help plz?

Thx

- Calculus -
**Reiny**, Tuesday, June 1, 2010 at 8:03pmfirst of all, to "solve" we need an equation.

You have the expression e^x - 2

Are you solving e^x - 2 = 0 ?

I will assume you are.

let f(x) = e^x - 2

f ' (x) = e^x

Newton's method says ...

x_{n+1}= x_{n}- f(x_{n})/f ' (x_{n})

so x_{2}= 1 - (e^1 - 2)/e^1

= .73576

x_{3}= .73576 - (e^.73576 - 2)/e^.73576 = .69404

x_{4}= .69404 - (e^.69404 - 2)/e^.69404 = .69314758

notice we are rapidly approaching some kind of fixed value.

If the value of x of our input returns as output, we have the solution.

A most remarkable procedure.

Using logs I get x = .69314718 , so our method was accurate to 6 digits after only 3 iterations.

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