Question

Find the Rates of convergence of the following functions as h->0

lim
h->0 sin h - hcosh
------------- = 0
h
Find the Rates of convergence of the following functions as n->inf

lim (Sin (1/n))^2=0
n-> inf

Answer 1

lim
h->0 (sin h - hcosh)/h

Use L'Hopital's rule. The ratio of derivatives of numerator and denominator is
cosh - h*cosh - h*sinh

and that approaches 1 as h -> 0

Answer 2

im asking the rate of convergence as the order such h^2? h^3? etc