Question

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

Options

• \[\lim_{x\to a^+}f(x)=f(a)\]

• \[\lim_{x\to a}f(x)\ne f(a)\]

• \[\lim_{x\to a^-}f(x)=f(a)\]

• \[\lim_{x\to b^-}f(x)=f(a)\]

Answer 1

At the left endpoint, values in the interval approach \[a\] only from the right. Hence only \[\lim_{x\to a^+}f(x)\] is considered.