# Find limx→af(x) from the given graph.

Question
Functions
Find $$\displaystyle\lim{x}→{a}{f{{\left({x}\right)}}}$$ from the given graph.

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
$$\displaystyle\lim{x}\to{a}{f{{\left({x}\right)}}}={b}.$$

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