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K Prove that lim f(x) = 7 if f(x) = { X-1 9-2x x<1 10x-3 x≥1 For a function f(x) that is defined in an open interval about c, except possibly at c itself, the limit of f(x) as x approaches c is the number L if, for every number e > 0, there exists a corresponding number 8>0 such that for all x, 0

K Prove that lim f(x) = 7 if f(x) = { X-1 9-2x x<1 10x-3 x≥1 For a function f(x) that is defined in an open interval about c, except possibly at c itself, the limit of f(x) as x approaches c is the number L if, for every number e > 0, there exists a corresponding number 8>0 such that for all x, 0

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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K Prove that lim f(x) = 7 if f(x) = { x-1 9-2x x<1 10x-3 x≥1 For a function f(x) that is defined in an open interval about c, except possibly at c itself, the limit of f(x) as x approaches c is the number L if, for every number e > 0, there exists a corresponding number 8>0 such that for all x, 0<x-c<8 implies that f(x)-L<e. To prove the given limit statement, it is necessary to show that for all x, if 0 < x-<8, then |(9-2x)-<e and (10x-3)-<e.
Transcribed Image Text:K Prove that lim f(x) = 7 if f(x) = { x-1 9-2x x<1 10x-3 x≥1 For a function f(x) that is defined in an open interval about c, except possibly at c itself, the limit of f(x) as x approaches c is the number L if, for every number e > 0, there exists a corresponding number 8>0 such that for all x, 0<x-c<8 implies that f(x)-L<e. To prove the given limit statement, it is necessary to show that for all x, if 0 < x-<8, then |(9-2x)-<e and (10x-3)-<e.
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