Confirming Continuity over an Interval
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Is
f
(
x
)
=
∣
x
∣
f(x) = |x|
f
(
x
)
=
∣
x
∣
continuous at
x
=
0
x = 0
x
=
0
?
QUESTION
Determine continuity of
f
(
x
)
=
1
x
f(x) = \frac{1}{x}
f
(
x
)
=
x
1
at
x
=
0
x = 0
x
=
0
.
QUESTION
What is
lim
x
→
2
(
x
2
−
4
)
/
(
x
−
2
)
\text{lim}_{x \to 2} (x^2 - 4)/(x - 2)
lim
x
→
2
(
x
2
−
4
)
/
(
x
−
2
)
?
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ANSWER
The limit is
4
4
4
, indicating a removable discontinuity. Factor
(
x
−
2
)
(
x
+
2
)
(x-2)(x+2)
(
x
−
2
)
(
x
+
2
)
and cancel to get
lim
x
→
2
(
x
+
2
)
=
4
\lim_{x \to 2} (x+2) = 4
lim
x
→
2
(
x
+
2
)
=
4
.
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