Question

Which sequence correctly checks continuity at \[x=c\]?

Options

• Find \[f(c)\], find \[\lim_{x\to c^-}f(x)\], find \[\lim_{x\to c^+}f(x)\], and compare them.

• Find \[\lim_{x\to c^+}f(x)\], then find only \[\lim_{x\to c^-}f(x)\].

• Find \[\lim_{x\to c}f(x)\], find \[f(c)\], and do not compare them.

• Find \[f(c)\], then conclude that \[f\] is continuous.

Answer 1

The continuity test first finds the function value and both one-sided limits. The function is continuous precisely when \[\text{LHL}=\text{RHL}=f(c)\].