# (a) Experiment with (14) for integer n. Using graphs, find out from which x = x n on the curves of (11) and (14) practically coincide. How does x n change with n? (b) What happens in (b) if n = ±1/2? (Our usual notation in this case would be v.) (c) How does the error of (14) behave as

Chapter 5, PROBLEM SET 5.4 #12

(a) Experiment with (14) for integer n. Using graphs, find out from which x = x_{n} on the curves of (11) and (14) practically coincide. How does x_{n} change with n?

(b) What happens in (b) if n = ±1/2? (Our usual notation in this case would be v.)

(c) How does the error of (14) behave as a function of x for fixed n? [Error = exact value minus approximation (14).]

(d) Show from the graphs that J_{0}(x) has extrema where J_{1}(x) = 0. Which formula proves this? Find further relations between zeros and extrema.

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