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