Defining Continuity at a Point
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
Check continuity of
f
(
x
)
=
1
x
f(x) = \frac{1}{x}
f
(
x
)
=
x
1
at
x
=
1
x = 1
x
=
1
.
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
.
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ANSWER
Removable discontinuity at
x
=
2
x = 2
x
=
2
. Factor gives
lim
x
→
2
(
x
+
2
)
=
4
\lim_{x \to 2} (x+2) = 4
lim
x
→
2
(
x
+
2
)
=
4
but
f
(
2
)
f(2)
f
(
2
)
undefined.
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