Mathematics

Problem

A function

f

is said to be continuous at

x=c

when which of the following sets of conditions are satisfied? a)

f(c)

exists and

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

exists b)

f(c)

exists,

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

exists, and

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

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

and

f(c)

exists d)

f'(c)

exists