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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 ɛ (this says 'f(x) is close to L') has been replaced by f(x) 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’.)

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 ɛ (this says 'f(x) is close to L') has been replaced by f(x) 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’.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Using only e's and 8's, and without using any limit rules, prove that x2 — бх + 7 lim 2. Definition: Let a E R 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 8 such that, for all real x with |x- a| < 8 andx#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 ɛ (this says 'f(x) is close to L') has been replaced by f(x) 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'.)
Transcribed Image Text:Using only e's and 8's, and without using any limit rules, prove that x2 — бх + 7 lim 2. Definition: Let a E R 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 8 such that, for all real x with |x- a| < 8 andx#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 ɛ (this says 'f(x) is close to L') has been replaced by f(x) 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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