Find limx→af(x) from the given graph.

Question
Functions
asked 2021-02-21
Find \(\displaystyle\lim{x}→{a}{f{{\left({x}\right)}}}\) from the given graph.

Answers (1)

2021-02-22
From the given graph we see that if we approach the point x=a from the left side the function f(x) approaches the point b from the downside of the curve. It follows that
\(\displaystyle\lim{x}\to{a}{f{{\left({x}\right)}}}={b}\)
Again we see that if we approach the point x=a from the right side the function f(x) approaches the point bb from the upside of the curve. That means,
\(\displaystyle\lim{x}\to{a}{f{{\left({x}\right)}}}={b}\)
Further note that f(a)=b. Therefore we get
\(\displaystyle\lim{x}\to{a}{f{{\left({x}\right)}}}={b}.\)
0

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