Determining Limits Using Algebraic Manipulation
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Find the limit of
f
(
x
)
=
x
2
−
4
x
+
4
f(x) = x^2 - 4x + 4
f
(
x
)
=
x
2
−
4
x
+
4
as
x
x
x
approaches 2.
QUESTION
State the limit of
f
(
x
)
=
x
2
−
9
x
−
3
f(x) = \frac{x^2 - 9}{x - 3}
f
(
x
)
=
x
−
3
x
2
−
9
as
x
x
x
approaches 3.
QUESTION
Evaluate
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:
(
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
, then substitute
x
=
1
x = 1
x
=
1
.
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