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, . . ., 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
Chapter 5, PROBLEM SET 5.5 #10
It can be shown that for large x,
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 = xn on 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)?
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