Question

Find the rate of convergence:
lim(h->inf) (sinh- hcosh)/h = 0
(using taylor series)

Answer 1

Hint: \[\frac{ \sin(h) }{ h } = 1\]

Answer 2

so that simplifies to...

lim(h->0) 1-cos(h) = 0

Answer 3

taylor expansion of (1-cos(x))...

1-cos(x) + sin(x)h + cos(x)h^2/2! - sin(x)h^3/3! - cos(x)h^4/4!... (?)

Answer 4

which then...

1-1 + 0 + h^2/2! - 0

Answer 5

so rate of convergence = O(h^2)

[i think?]