Connecting Infinite Limits and Vertical Asymptotes
AP Calculus BC · Flashcards · Recall
AP CALCULUS BC · FLASHCARDS
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QUESTION
What is the behavior of
f
(
x
)
f(x)
f
(
x
)
near a vertical asymptote at
x
=
a
x = a
x
=
a
?
QUESTION
What behavior does
f
(
x
)
=
1
x
2
f(x) = \frac{1}{x^2}
f
(
x
)
=
x
2
1
exhibit as
x
→
0
x \to 0
x
→
0
?
QUESTION
State the condition for a vertical asymptote at
x
=
a
x = a
x
=
a
for
f
(
x
)
=
P
(
x
)
Q
(
x
)
f(x) = \frac{P(x)}{Q(x)}
f
(
x
)
=
Q
(
x
)
P
(
x
)
.
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ANSWER
Q
(
a
)
=
0
Q(a) = 0
Q
(
a
)
=
0
and
P
(
a
)
≠
0
P(a) \neq 0
P
(
a
)
=
0
. Denominator zero but numerator nonzero creates division by zero.
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