Mathematics

Problem

Which set of requirements is BOTH necessary and sufficient for a function

f

to be continuous at

x=c

? a)

f(c)

is defined and

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

exists. b)

f(c)

is defined,

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

exists, and

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

. c)

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

exists and equals

f(c)

, whether or not

f(c)

is defined separately. d)

f'(c)

exists.