Using only e's and d's, and without using any limit rules, prove that x² – 6x+7 lim = 2. Definition: Let a ER and f : R \ {a} → R be a function. We say that f(x) → +o as x→ a if and only if for every real number M there exists a positive & such that, for all real x with |x- a| < 8 and x#a, we have f(x) > M. Notice the similarities between this and Ross (1), page 160. The inequality |f(x) – L| < ɛ (this says 'f(x) is close to L') has been replaced by f(x) > M (this says 'f(x) is large’.)

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