Algebraic Properties of Limits
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Find
lim
x
→
4
x
2
−
16
x
−
4
\text{lim}_{x \to 4} \frac{x^2 - 16}{x - 4}
lim
x
→
4
x
−
4
x
2
−
16
. Use algebraic properties.
QUESTION
What is the limit property for a constant multiple:
If
lim
x
→
a
f
(
x
)
=
L
\text{If }\text{lim}_{x \to a} f(x) = L
If
lim
x
→
a
f
(
x
)
=
L
, what is
lim
x
→
a
[
c
f
(
x
)
]
\text{lim}_{x \to a} [cf(x)]
lim
x
→
a
[
c
f
(
x
)]
?
QUESTION
Find
lim
x
→
−
2
x
2
+
4
x
+
4
x
+
2
\text{lim}_{x \to -2} \frac{x^2 + 4x + 4}{x + 2}
lim
x
→
−
2
x
+
2
x
2
+
4
x
+
4
. Use algebraic properties.
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ANSWER
The limit is
−
4
-4
−
4
. Factor perfect square:
(
x
+
2
)
2
x
+
2
=
x
+
2
\frac{(x+2)^2}{x+2} = x+2
x
+
2
(
x
+
2
)
2
=
x
+
2
, then substitute.
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