Algebraic Properties of Limits
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
Find
lim
x
→
−
1
(
x
3
+
4
x
2
+
x
−
6
)
\text{lim}_{x \to -1} (x^3 + 4x^2 + x - 6)
lim
x
→
−
1
(
x
3
+
4
x
2
+
x
−
6
)
. Use algebraic properties.
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
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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