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