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 Y_{0}(x) from your CAS and from (11). How does the error behave as m increases?

(d) Do (c) for Y_{1}(x) and Y_{2}(x). How do the errors compare to those in (c)?

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