Defining Continuity at a Point
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
For
f
(
x
)
=
2
x
+
3
f(x) = 2x + 3
f
(
x
)
=
2
x
+
3
, is
f
(
x
)
f(x)
f
(
x
)
continuous for all
x
x
x
?
QUESTION
Is
f
(
x
)
=
sgn
(
x
)
f(x) = \text{sgn}(x)
f
(
x
)
=
sgn
(
x
)
continuous at
x
=
0
x = 0
x
=
0
?
QUESTION
Determine the type of discontinuity:
f
(
x
)
=
1
x
f(x) = \frac{1}{x}
f
(
x
)
=
x
1
at
x
=
0
x = 0
x
=
0
.
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ANSWER
Non-removable (infinite) discontinuity at
x
=
0
x = 0
x
=
0
. Function approaches infinity at
x
=
0
x=0
x
=
0
, creating an unbounded discontinuity.
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