It can be shown that for large x,with ∼ defined

It can be shown that for large x,

Y,(x) ~ V2/(TX) sin (x – }nn - 7)

with ˆ¼ defined as in (14) of Sec. 5.4.

(a) Graph Yn for n = 0, . . ., 5 on common axes. Are there relations between zeros of one function and extrema of another? For what functions?

(b) Find out from graphs from which x = xon the curves of (8) and (11) (both obtained from your CAS) practically coincide. How does xn change with n?

(c) Calculate the first ten zeros xm, m = 1, . . ., 10 of Y0(x) from your CAS and from (11). How does the error behave as m increases?

(d) Do (c) for Y1(x) and Y2(x). How do the errors compare to those in (c)?