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Mathematics
Problem
Which one of the following statements is the necessary and sufficient condition for a real function
f
f
f
to be continuous at
x
=
c
x=c
x
=
c
? a)
lim
x
→
c
f
(
x
)
exists
\displaystyle \lim_{x\to c} f(x)\text{ exists}
x
→
c
lim
f
(
x
)
exists
b)
f
f
f
is differentiable at
x
=
c
x=c
x
=
c
c)
lim
x
→
c
f
(
x
)
=
f
(
c
)
\displaystyle \lim_{x\to c} f(x)=f(c)
x
→
c
lim
f
(
x
)
=
f
(
c
)
d)
lim
x
→
c
−
f
(
x
)
=
lim
x
→
c
+
f
(
x
)
\displaystyle \lim_{x\to c^-} f(x)=\lim_{x\to c^+} f(x)
x
→
c
−
lim
f
(
x
)
=
x
→
c
+
lim
f
(
x
)
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