Defining Continuity at a Point
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
What is the conclusion if
lim
x
→
c
f
(
x
)
=
f
(
c
)
\text{lim}_{x \to c} f(x) = f(c)
lim
x
→
c
f
(
x
)
=
f
(
c
)
and
f
(
c
)
f(c)
f
(
c
)
is defined?
QUESTION
Find if
f
(
x
)
=
x
2
−
4
x
−
2
f(x) = \frac{x^2 - 4}{x - 2}
f
(
x
)
=
x
−
2
x
2
−
4
is continuous at
x
=
2
x = 2
x
=
2
.
QUESTION
Which condition fails if
lim
x
→
c
f
(
x
)
≠
f
(
c
)
\text{lim}_{x \to c} f(x) \neq f(c)
lim
x
→
c
f
(
x
)
=
f
(
c
)
?
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ANSWER
The condition that
lim
x
→
c
f
(
x
)
=
f
(
c
)
\text{lim}_{x \to c} f(x) = f(c)
lim
x
→
c
f
(
x
)
=
f
(
c
)
. The limit and function value don't match.
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