Question: Suppose that a R and / is an open interval which contains a. If f : I R satisfies f(x) f(a), as

Suppose that a ∊ R and / is an open interval which contains a. If f : I → R satisfies f(x) → f(a), as x → a, and if there exist numbers M and m such that m < f(a) < M, prove that there exist positive numbers ∊ and δ such that
m + ∊ < f(x) < M - ε
for all JC'S which satisfy |JC - a\ < 8

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