Continuity - Limits


The idea of continuity lies in many things we experience in our daily lives, for instance, the time it takes you to log into StudyPug and read this section. Limits and continuity are so related that we cannot only learn about one and ignore the other. We will learn about the relationship between these two concepts in this section.


A function f is continuous at a number a, if and only if:
limxaf(x)=limxa+f(x)=f(a)\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x) = f(a)
graph of a continuous function (a)
In simple words, the graph of a continuous function has no break in it and can be drawn without lifting your pen from the paper.
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