Question

If \[f\] is defined on the closed interval \[[a,b]\], which condition establishes continuity at the right endpoint \[b\]?

Options

• \[\lim_{x\to b^-}f(x)=f(b)\]

• \[\lim_{x\to a^+}f(x)=f(b)\]

• \[\lim_{x\to b}f(x)\ne f(b)\]

• \[\lim_{x\to b^+}f(x)=f(b)\]

Answer 1

At the right endpoint, values in the interval approach \[b\] only from the left. Thus the appropriate condition is \[\lim_{x\to b^-}f(x)=f(b)\].