Question

Which is a necessary condition for continuity at \[x=c\]?

Options

• \[\lim_{x\to c}f(x)\] must not exist.

• \[f(c)\] must be defined.

• The left-hand limit and right-hand limit must not be equal.

• \[f(c)\] must not be defined.

Answer 1

The value \[f(c)\] is part of the condition \[\lim_{x\to c}f(x)=f(c)\]. Therefore, a function cannot be continuous at \[c\] unless \[f(c)\] is defined.