Connecting Infinite Limits and Vertical Asymptotes
AP Calculus AB · Flashcards · Recall
AP CALCULUS AB · FLASHCARDS
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QUESTION
What does
lim
x
→
a
+
f
(
x
)
=
infinity
\text{lim}_{x \to a^+} f(x) = \text{infinity}
lim
x
→
a
+
f
(
x
)
=
infinity
tell about
f
(
x
)
f(x)
f
(
x
)
?
QUESTION
What is the condition for a vertical asymptote at
x
=
a
x = a
x
=
a
in
f
(
x
)
=
p
(
x
)
q
(
x
)
f(x) = \frac{p(x)}{q(x)}
f
(
x
)
=
q
(
x
)
p
(
x
)
?
QUESTION
What happens if
lim
x
→
a
−
f
(
x
)
=
−
infinity
\text{lim}_{x \to a^-} f(x) = -\text{infinity}
lim
x
→
a
−
f
(
x
)
=
−
infinity
?
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ANSWER
f
(
x
)
f(x)
f
(
x
)
has a vertical asymptote at
x
=
a
x = a
x
=
a
. Left-sided negative limit confirms vertical asymptote.
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