Selecting Procedures for Determining Limits
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Evaluate the limit:
lim
x
→
∞
2
x
+
3
5
x
−
4
\lim_{x \to \infty} \frac{2x + 3}{5x - 4}
lim
x
→
∞
5
x
−
4
2
x
+
3
.
QUESTION
What is the limit of
ln
(
x
)
\text{ln}(x)
ln
(
x
)
as
x
x
x
approaches Infinity?
QUESTION
What is the limit of
x
2
−
1
x
−
1
\frac{x^2 - 1}{x - 1}
x
−
1
x
2
−
1
as
x
x
x
approaches 1?
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ANSWER
2. Factor numerator:
(
x
+
1
)
(
x
−
1
)
x
−
1
=
x
+
1
\frac{(x+1)(x-1)}{x-1} = x+1
x
−
1
(
x
+
1
)
(
x
−
1
)
=
x
+
1
, so limit is
1
+
1
=
2
1+1=2
1
+
1
=
2
.
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