I have no idea what you are doing.
Just compute .
Where
And and .
I have found the first 5 Taylor polynomials about x=0 for cosh(x). Being p0=1, p1=1, p2=1+ , p3=1+ , p4=1+ + .
How do I Find the Maclaurin series for cosh(x)?
I can see it should be something like
but how can I show a methodic way to get there from the polynomial approximations?
Also, how do I use Landau's big O notation to find
I simplify this with identity to
then change them to Maclaurin approximations with big O error.
How do I simplify that expression to get the limit?
Thank you for any help.
I know how to do the big O problem now.. it was trivial. divide through by x^2 and let x tend to 0. yielding the limit -4/9
I know how to get the polynomials, I've worked them out. I need a way to find the series from the polynomials. I don't want to just write down. This is the series I found for cosh(x) through google which makes sense.
(there should be an infinity symbol above the sum)
I want to get to that series from the Maclaurin polynomials which I have calculated if possible.
Would finding the series for the nth polynomial help? I'm confused by the fact that every second step yields a 0 term and how that translates to the Maclaurin series. I know the formula I'm just having trouble applying it. The definition has the nth derivative in it but then in the examples it's always an infinite series that looks similar to the series for the nth polynomial.