MATH137 Lecture Notes - Lecture 4: Algebraic Function, Paula Smith, Squeeze Theorem

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MATH137 Full Course Notes
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Math 137 week 4 notes dr. paula smith: calculating limits (2. 3, limit laws, basics, limx k = k where k is a constant. Then for any > 0, 0 < |x a| < |f(x) l| = |k k| = 0 < : limx x = . Then 0 < |x a| < |f(x) l| = |x a| < : suppose f(x) l and g(x) m , as x a. M: root law: limx [f(x)]n = [lim x f(x)] n at x = l, proof of sum law (other proofs found in app. We wish to prove lim x (f(x)+ g(x)) = l + m if lim x f(x) = l and lim x g(x)= m. Because lim x f(x) = l, given 1 = /2, there is 1 > 0 such that if 0 < |x a| < 1 then |f(x) l| < 1.

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