Connecting Differentiability and Continuity
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Find if
f
(
x
)
=
sgn
(
x
)
f(x) = \text{sgn}(x)
f
(
x
)
=
sgn
(
x
)
is continuous at
x
=
0
x=0
x
=
0
.
QUESTION
Is the function
f
(
x
)
=
1
x
f(x) = \frac{1}{x}
f
(
x
)
=
x
1
differentiable at
x
=
0
x=0
x
=
0
?
QUESTION
Determine if
f
(
x
)
=
sin
(
x
)
f(x) = \text{sin}(x)
f
(
x
)
=
sin
(
x
)
is differentiable at
x
=
0
x=0
x
=
0
.
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ANSWER
Yes,
f
(
x
)
=
sin
(
x
)
f(x) = \text{sin}(x)
f
(
x
)
=
sin
(
x
)
is differentiable at
x
=
0
x=0
x
=
0
. Sine function is smooth and differentiable everywhere.
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