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

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

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

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

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