Confirming Continuity over an Interval
AP Calculus BC · Flashcards · Recall
AP CALCULUS BC · FLASHCARDS
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QUESTION
What must be true for a function's one-sided limits at
x
=
a
x = a
x
=
a
for continuity?
QUESTION
What is a removable discontinuity?
QUESTION
State the three conditions for continuity at a point.
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ANSWER
f
(
a
)
f(a)
f
(
a
)
is defined,
lim
x
→
a
f
(
x
)
\text{lim}_{x \to a} f(x)
lim
x
→
a
f
(
x
)
exists,
lim
x
→
a
f
(
x
)
=
f
(
a
)
\text{lim}_{x \to a} f(x) = f(a)
lim
x
→
a
f
(
x
)
=
f
(
a
)
. All three must hold for continuity to be confirmed.
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