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For each of the following limits, a value of € is given. For each, give the largest value of 6 which makes the sentence: For all x € R, if 0 < x- c < 8 then |f(x) - L| < € a true sentence. (a) lim 5x6 = 9, where e = 1. x-3 (b) lim √x = 2, where € = 1. x-4 (c) lim [x] = 3, where = 1. (The function [x] is the "floor", or "integer XIT part" function, which outputs the greatest integer which is less than or equal to x.)

For each of the following limits, a value of € is given. For each, give the largest value of 6 which makes the sentence: For all x € R, if 0 < x- c < 8 then |f(x) - L| < € a true sentence. (a) lim 5x6 = 9, where e = 1. x-3 (b) lim √x = 2, where € = 1. x-4 (c) lim [x] = 3, where = 1. (The function [x] is the "floor", or "integer XIT part" function, which outputs the greatest integer which is less than or equal to x.)

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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For each of the following limits, a value of € is given. For each, give the largest value of which makes the sentence: For all x € R, if 0 < x − c < 6 then |ƒ(x) − L| < € a true sentence. (a) lim 5x − 6 = 9, where € = 1. - x →3 (b) lim √x = 2, where € = 1. x (c) lim [x] = 3, where € = 1. (The function [x] is the "floor", or "integer X-T part" function, which outputs the greatest integer which is less than or equal to x.)
Transcribed Image Text:For each of the following limits, a value of € is given. For each, give the largest value of which makes the sentence: For all x € R, if 0 < x − c < 6 then |ƒ(x) − L| < € a true sentence. (a) lim 5x − 6 = 9, where € = 1. - x →3 (b) lim √x = 2, where € = 1. x (c) lim [x] = 3, where € = 1. (The function [x] is the "floor", or "integer X-T part" function, which outputs the greatest integer which is less than or equal to x.)
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