Removing Discontinuities
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
What is the removable discontinuity in
f
(
x
)
=
x
2
−
25
x
−
5
f(x) = \frac{x^2 - 25}{x - 5}
f
(
x
)
=
x
−
5
x
2
−
25
?
QUESTION
Determine if
f
(
x
)
=
x
2
−
9
x
−
3
f(x) = \frac{x^2 - 9}{x - 3}
f
(
x
)
=
x
−
3
x
2
−
9
is continuous at
x
=
3
x = 3
x
=
3
.
QUESTION
How do you simplify
f
(
x
)
=
x
2
−
1
x
−
1
f(x) = \frac{x^2 - 1}{x - 1}
f
(
x
)
=
x
−
1
x
2
−
1
?
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ANSWER
x
+
1
x + 1
x
+
1
, after factoring and canceling
(
x
−
1
)
(x-1)
(
x
−
1
)
. Factor
x
2
−
1
=
(
x
−
1
)
(
x
+
1
)
x^2-1=(x-1)(x+1)
x
2
−
1
=
(
x
−
1
)
(
x
+
1
)
to cancel
(
x
−
1
)
(x-1)
(
x
−
1
)
and get
x
+
1
x+1
x
+
1
.
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