(adsbygoogle = window.adsbygoogle || []).push({}); The problem statement, all variables and given/known data

Let f be a function with the property that every point of discontinuity is a removable discontinuity. This means that [tex]\lim_{y\to x} f(y)[/tex] exists for all x, but f may be discontinuous at some (even infinitely many) numbers x. Define [tex]g(x) = \lim_{y\to x} f(y)[/tex]. Prove that g is continuous.

The attempt at a solution

So I have to prove that for all a,

[tex]\lim_{x \to a} g(x) = \lim_{x \to a} \lim_{y\to x} f(y) = g(a) = \lim_{y\to a} f(y) [/tex]

In other words, for every e > 0, there is a d > 0 such that

[tex]\left| \lim_{y\to x} f(y) - \lim_{y\to a} f(y) \right| < e[/tex]

for all x satisfying |x - a| < d. I have no clue how to find d. Any tips.

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# Homework Help: A Continuity Problem

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