Limits at Infinity and Horizontal Asymptotes
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Find the limit as
x
x
x
approaches infinity for
f
(
x
)
=
7
x
3
2
x
3
+
5
f(x) = \frac{7x^3}{2x^3 + 5}
f
(
x
)
=
2
x
3
+
5
7
x
3
.
QUESTION
Find the horizontal asymptote of
f
(
x
)
=
3
x
+
2
4
x
+
5
f(x) = \frac{3x + 2}{4x + 5}
f
(
x
)
=
4
x
+
5
3
x
+
2
.
QUESTION
What is the limit as
x
x
x
approaches infinity for
f
(
x
)
=
2
x
+
1
3
x
+
4
f(x) = \frac{2x + 1}{3x + 4}
f
(
x
)
=
3
x
+
4
2
x
+
1
?
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ANSWER
2
3
\frac{2}{3}
3
2
. Same degree; ratio of leading coefficients is
2
3
\frac{2}{3}
3
2
.
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