Discover the Power of Maclaurin Series: A Comprehensive Guide

[irunshow]

solved thanks

 

[Dick]

Yes, the first part is correct. The limit of the ratios is 0 so the radius of convergence is infinite. For the second part you need a form for the remainder term in a Taylor series. Weren't you given one? If not look it up and try to estimate it.

 

[irunshow]

Thanks Dick,

Yea my teacher didnt explain it in class cause there was no time left.
Is there a general formula to calculate the max error?

Thanks

 

[Dick]

Try http://en.wikipedia.org/wiki/Taylor's_theorem#Explicit_formulae_for_the_remainder I'm looking at the Lagrange remainder form. You have to try and estimate it's maximum value for x in [-.5,.5].

 

[irunshow]

Hey dick,

thanks but i think my teachers wants to do it with this formula:

abs(Rn(x)) less than or equal to (M)/(n+1)! abs(x-a)^(n+1)

I don't know what the M equals to tho

 

[Dick]

Hey dick,

thanks but i think my teachers wants to do it with this formula:

abs(Rn(x)) less than or equal to (M)/(n+1)! abs(x-a)^(n+1)

I don't know what the M equals to tho

M is a bound for the k+1 derivative of f(x) over the interval. Look at the link I sent you. You'll see f^(k+1) instead of M.

 

[irunshow]

Hi i got the answer to be 0.0317.
Is that correct?

Thanks =)

 

[Dick]

solved thanks

Don't delete the problem after you've solved it! Other people with similar problems are supposed to be able to search for previous threads that can help them. Deleting parts of it defeats that.

 

[irunshow]

edit: kk i won't next time xD