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Given a function f: A→ R and a real number e that is a limit point of A. We say that ilm-f(x) = L ("the ilmit of f as z approaches e is L"). provided: There is a d>0 such that for all > 0, and for all z € A if 0 <\x_c<8/ then f(x)-L

Given a function f: A→ R and a real number e that is a limit point of A. We say that ilm-f(x) = L ("the ilmit of f as z approaches e is L"). provided: There is a d>0 such that for all > 0, and for all z € A if 0 <\x_c<8/ then f(x)-L

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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6. Given a function f: A → R and a real number e that is a limit point of A. We say that ilm-f(x) = L ("the ilmit of f as r approaches c is L"). provided: There is a d>0 such that for all e > 0, and for all z € A if 0 <\x-c| < 8 then f(x)-L<E. Prove or disprove that ilm-f(x) = L is equivalent to limz-e f(x) = L.
Transcribed Image Text:6. Given a function f: A → R and a real number e that is a limit point of A. We say that ilm-f(x) = L ("the ilmit of f as r approaches c is L"). provided: There is a d>0 such that for all e > 0, and for all z € A if 0 <\x-c| < 8 then f(x)-L<E. Prove or disprove that ilm-f(x) = L is equivalent to limz-e f(x) = L.
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