Mathematics

Problem

Which of the following collections of statements is both necessary and sufficient to guarantee that a function

f

is continuous at

x=c

? I.

f(c)

exists. II.

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

exists. III.

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

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