I've been trying to figure out how to do the question in the attached file for quite a few days now, and I think I've got most of it figured out. I need to find the rate of convergence of the function as h approaches 0. I have attached both the question and my work. I'm down to the final inequality and have no idea how to find O(h^2) which is the answer to this question.
The function is lim h->0 (sinh+hcosh)/h
Any help would be appreciated.