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We have lim 1 0, but - n-0 n lim f) 1 lim 1 = 1+0 = f(0). Thus n by Theorem 9.2.1, f is not continuous at 0. Problem 9.2.3. Use Theorem 9.2.1 to show that Theorem 9.2.1. The function f is continuous at a if and only if f satisfies the following property: V sequences (n), if lim xn = a then lir

We have lim 1 0, but - n-0 n lim f) 1 lim 1 = 1+0 = f(0). Thus n by Theorem 9.2.1, f is not continuous at 0. Problem 9.2.3. Use Theorem 9.2.1 to show that Theorem 9.2.1. The function f is continuous at a if and only if f satisfies the following property: V sequences (n), if lim xn = a then lir

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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Problem 9.2.3 real math analysis 

12:19 M we need to do Is create a single sequence (Xn)which converges to 0, but for which the sequence (f (xn)) does not converge to f(0) = 0. For a function like this one, just about any sequence will do, but let's use (-), just because it is an old familiar friend. We have lim 1 0, but n→00 n lim f = lim 1 = 1 0 = f(0). Thus n by Theorem 9.2.1, f is not continuous at 0. Problem 9.2.3. Use Theorem 9.2.1 to show that Theorem 9.2.1. The function f is continuous at a if and only if f satisfies the following property: sequences (xn), if lim xn = a then lir in-context if x + 0 f(x) = if x is not continuous at 0, no matter what value a is. II II
Transcribed Image Text:12:19 M we need to do Is create a single sequence (Xn)which converges to 0, but for which the sequence (f (xn)) does not converge to f(0) = 0. For a function like this one, just about any sequence will do, but let's use (-), just because it is an old familiar friend. We have lim 1 0, but n→00 n lim f = lim 1 = 1 0 = f(0). Thus n by Theorem 9.2.1, f is not continuous at 0. Problem 9.2.3. Use Theorem 9.2.1 to show that Theorem 9.2.1. The function f is continuous at a if and only if f satisfies the following property: sequences (xn), if lim xn = a then lir in-context if x + 0 f(x) = if x is not continuous at 0, no matter what value a is. II II
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