(Solution) - Suppose that f is a real function a Prove that if exists -(2025 Original AI-Free Solution)

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Suppose that f is a real function.
a) Prove that if

Suppose that f is a real function.
a) Prove that if
exists,
exists, then |f(x)| ? |L| as x ? a.
b) Show that there is a function such that, as x ? a, |f(x)| ? |L| but the limit of f (x) does not exist.