Consider the function defined for 0 < x < 1

f(x)1 if 10 n < x < 10 n and n is an even positive integer = if 10 n < x < 10 n and n is an odd positive integer.

(a) What it the value f(x) for x = 0.9, x = 0.05, and x = 0.003?

(b) For every e > 0 and every 5 > 0 there exists an 0 < x < 5 so that 11(x) — 11 < a

(c) Prove that the statement lira f(x) = 1 is false. You may only use the precise definition of a limit (e-5 definition). You are not allowed to use

limit laws.

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