Wednesday

October 22, 2014

October 22, 2014

Posted by **Janet** on Sunday, April 17, 2011 at 3:19pm.

This is what I did, but not working.

f'(x)=e^x-5

x2=1.5 - (e^1.5-(5(1.5))/e^1.5 -(5))

=1.5-(4.4817-7.5/4.4817-5)=1.5-5.8234= -4.3234

x3=-4.3234-(e^-4.3234-(5(-4.3234))/ e^-4.3234-(5)) = -4.3234-(21.630/-4.987)= -4.3234-(-4.337)=.0136

I did another one for x4, but the number was no where near either of these two. Aren't they suppose to be somewhat close? Did I make a dumb algebra mistake or am I not doing this right at all?

- Calculus -
**MathMate**, Sunday, April 17, 2011 at 3:49pmOn the contrary, your equations and calculations are good.

For X1=1.5

I get

x2=-4.32

x3=0.01415

x4=0.250868

Your x4 is quite close to the exact answer of 0.25917110181907.

In fact, by x7, you will get the answer accurate to 14 decimal places.

This exercise is probably to illustrate that the Newton's method converges "no matter what", at least in this case where the function has the same concavity within the range.

**Answer this Question**

**Related Questions**

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

Calculus - Use five iterations in Newton’s method to estimate the root of cos(2x...

Calculus 1 Newton's Method - Using Newton's method, approximate the root of the ...

Calculus - Use Newton’s method to approximate the root of x^2 + 4x + 2 = 0 ...

calculus - Use Newton's method to approximate the indicated root of the equation...

Calculus 1 - Use Newton's method to approximate the root of the equation x^3+x+2...

Calculus-Newton Method Approximation - Use Newton's method to approximate the ...

Using Matlab - imagine you have a simple calculator that can only do addition,...

calculus - Use Newton's method to solve the equation sec x = 4 in the interval x...

calculus - Use the Newton method to approximate the indicated zero of the ...