Question

Which conclusion establishes that \[f\] is continuous at \[x=c\]?

Options

• \[\lim_{x\to c}f(x)=f'(c)\]

• \[\lim_{x\to c}[f(x)-f(c)]=f'(c)\]

• \[\lim_{x\to c}f'(x)=f(c)\]

• \[\lim_{x\to c}f(x)=f(c)\]

Answer 1

Continuity at \[c\] means that the limit of the function as \[x\to c\] equals its value at \[c\]. The required equality is \[\lim_{x\to c}f(x)=f(c)\].