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2. Let f(r) = r² and let e > 0 be given. (a) Find ő so that z – 1| < 6 implies |f(z) – f(1)| < e. (b) Find ő so that |x – 2| < 6 implies |f(z) – f(2)| < e. (c) If n > 2 and you had to find a ô so that |r – n| < ó implies |f(x) – f(n)| < e, would ô be larger or smaller than the ó for parts (a) and (b)Why?.

2. Let f(r) = r² and let e > 0 be given. (a) Find ő so that z – 1| < 6 implies |f(z) – f(1)| < e. (b) Find ő so that |x – 2| < 6 implies |f(z) – f(2)| < e. (c) If n > 2 and you had to find a ô so that |r – n| < ó implies |f(x) – f(n)| < e, would ô be larger or smaller than the ó for parts (a) and (b)Why?.

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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#2. A, B, and C. Thanks. 

2. Let f(x) = x² and let e > 0 be given. (a) Find ő so that |r – 1| < ô implies |f(x) – f(1)| < e. (b) Find ő so that |æ – 2| < ô implies |f(x) – f(2)| < e. (c) If n > 2 and you had to find a d so that |x – n| < d implies |f(x) – f(n)| < €, would 8 be larger or smaller than the ổ for parts (a) and (b)Why?.
Transcribed Image Text:2. Let f(x) = x² and let e > 0 be given. (a) Find ő so that |r – 1| < ô implies |f(x) – f(1)| < e. (b) Find ő so that |æ – 2| < ô implies |f(x) – f(2)| < e. (c) If n > 2 and you had to find a d so that |x – n| < d implies |f(x) – f(n)| < €, would 8 be larger or smaller than the ổ for parts (a) and (b)Why?.
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