Mathematics

Problem

A function

f

is examined at

x=c

using the following statements. I.

f(c)

exists. II.

\displaystyle\lim_{x\to c}f(x)

exists. III.

\displaystyle\lim_{x\to c}f(x)=f(c)

. Which of the above statements must all be true to guarantee that

f

is continuous at

x=c

? a) I and II only b) II and III only c) I, II, and III d) I only