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Mathematics
Problem
Which of the following equalities is required for a function
f
f
f
to be continuous at the left-hand endpoint
x
=
a
x=a
x
=
a
of the closed interval
[
a
,
b
]
[a,b]
[
a
,
b
]
? 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)
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
)
=
f
(
a
)
\displaystyle\lim_{x\to a^{+}} f(x)=f(a)
x
→
a
+
lim
f
(
x
)
=
f
(
a
)
d)
lim
x
→
a
f
(
x
)
\displaystyle\lim_{x\to a} f(x)
x
→
a
lim
f
(
x
)
exists, irrespective of
f
(
a
)
f(a)
f
(
a
)
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