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Problem 7.1.2. Let a and b be real numbers with b > 0. Prove |a| < b if and only if -b < a < b. Notice that this can be extended to a| < b if and only if -b < a < b.

Problem 7.1.2. Let a and b be real numbers with b > 0. Prove |a| < b if and only if -b < a < b. Notice that this can be extended to a| < b if and only if -b < a < b.

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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Convergence of

Sequences of Real Numbers

Can you please help me solve 7.1.2

9:24 A A personal.psu.edu/ecb5/ASO formulations can be used to prove convergence. Depending on the application, one of these may be more advantageous to use than the others. 4. Any time an N can be found that works for a particular e, any number M > N will work for that ɛ as well, since if n > M then n > N. Problem 7.1.2. Let a and b be real numbers with b > 0. Prove la| < b if and only if -b < a < b. Notice that this can be extended to |a| < b if and only if -b < a < b. To illustrate how this definition makes the above ideas rigorous, let's use it to prove 1 - 0. that lim n→00 n 글. If n > N, then n > and so = - < e. = 0. Proof. Let ɛ > 0 be given. Let N Hence by definition, lim,→ Notice that this proof is rigorous and makes no reference to vague notions such as "getting smaller" or "approaching II II
Transcribed Image Text:9:24 A A personal.psu.edu/ecb5/ASO formulations can be used to prove convergence. Depending on the application, one of these may be more advantageous to use than the others. 4. Any time an N can be found that works for a particular e, any number M > N will work for that ɛ as well, since if n > M then n > N. Problem 7.1.2. Let a and b be real numbers with b > 0. Prove la| < b if and only if -b < a < b. Notice that this can be extended to |a| < b if and only if -b < a < b. To illustrate how this definition makes the above ideas rigorous, let's use it to prove 1 - 0. that lim n→00 n 글. If n > N, then n > and so = - < e. = 0. Proof. Let ɛ > 0 be given. Let N Hence by definition, lim,→ Notice that this proof is rigorous and makes no reference to vague notions such as "getting smaller" or "approaching II II
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