Question 18How do we transform lim (x- x*) in evaluating it. This yields an answer ofX+ 00(A) by direct substitution; answer = 0B multiply by its conjugate; Answer is + oby factoring; Answer is – oD) by factoring; Answer: does not exist

Answered: Image /qna-images/answer/fe6fa347-a4a4-4b77-a780-0ead3189bc34.jpg

Answered: Question 18 How do we transform lim…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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mathematically before reading the proof. (It might be helpful to read the discussion that follows Theorem 2.4 or to look at Appendix A.) THEOREM 3.2 THEIS a function that is defined on I except possibly at the point c. Let I be an open interval that contains the point c and suppose a) The function f has limit L at c if and only if for each sequence {Xn) in I\ {c} that converges to c, the sequence (f (x,)} converges to L. b) Suppose that there are sequences (x,} and (y,} in I\ {c} that converge to c such that {ƒ(xn)} converges to L, and (f(yn)} converges to L2. If Li + L2, then the functionf does not have a limit at c. Proof Let P be the statement "the function f has limit L at c" and let Q be the statement "for each sequence {xn} in I\ {c} that converges to c, the sequence (f(xn)} converges to L". A proof that P Q will be left as an exercise. To prove that Q = P, we will prove the contrapositive. Suppose lim f (x) # L. By the negation of the definition, there exists e>0 such that for…
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Question 18 How do we transform lim (x-- x*) in evaluating it. This yields an answer of. (A by direct substitution; answer = 0 multiply by its conjugate; Answer is + ∞ by factoring; Answer is – o D) by factoring; Answer: does not exist