Question
Let $f:(a, b) \rightarrow \mathbb{R}$ be monotone and let $a<x<b$. Show that $f$ is continuous at $x$ if and only if $f(x-)=f(x+)$.
Step 1
The left-hand limit is defined as: \[ f(x-) = \lim_{t \to x^-} f(t) \] and the right-hand limit is defined as: \[ f(x+) = \lim_{t \to x^+} f(t). \] Show more…
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limits and Continuity
Continuity
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