Connecting Infinite Limits and Vertical Asymptotes
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Identify the vertical asymptote in
f
(
x
)
=
1
x
−
2
f(x) = \frac{1}{x-2}
f
(
x
)
=
x
−
2
1
.
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
?
QUESTION
Find the vertical asymptotes of
f
(
x
)
=
x
x
2
−
9
f(x) = \frac{x}{x^2 - 9}
f
(
x
)
=
x
2
−
9
x
.
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ANSWER
Vertical asymptotes at
x
=
3
x = 3
x
=
3
and
x
=
−
3
x = -3
x
=
−
3
. Factor denominator:
x
2
−
9
=
(
x
−
3
)
(
x
+
3
)
=
0
x^2 - 9 = (x-3)(x+3) = 0
x
2
−
9
=
(
x
−
3
)
(
x
+
3
)
=
0
.
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