Suppose that f is a real function.a) Prove that ifexists, then | f (x)| → |L| as x → a.b)...

Suppose that f is a real function.

a) Prove that if

exists, then | f (x)| → |L| as x → a.

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b) Show that there is a function such that, as x → a, | f (x)| → |L| but the limit of f (x) does not exist.