1. Using only &'s and d's, and without using any limit rules, prove that x2 - 6x +7 lim = 2. x-+1 X Definition: Let a E R and f : R {a} - R be a function. We say that f (x) > too as x -> a if and only if for every real number M there exists a positive d such that, for all real x with |x - al M. Notice the similarities between this and Ross (1), page 160. The inequality If (x) - L| M (this says 'f (x) is large'.)