It can be shown that for large x, with ¼ defined as in (14) of Sec. 5.4. (a) Graph Y n for n = 0,

It can be shown that for large x,

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

(a) Graph Y_n 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 = x_n on the curves of (8) and (11) (both obtained from your CAS) practically coincide. How does x_n change with n?

(c) Calculate the first ten zeros x_m, 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)?

Y,(x) ~ V2/(TX) sin (x }nn - 7)