Connecting Differentiability and Continuity
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
For
f
(
x
)
=
1
x
f(x) = \frac{1}{x}
f
(
x
)
=
x
1
, is
f
(
x
)
f(x)
f
(
x
)
differentiable at
x
=
0
x = 0
x
=
0
?
QUESTION
What is the derivative rule for a sum
f
(
x
)
+
g
(
x
)
f(x) + g(x)
f
(
x
)
+
g
(
x
)
?
QUESTION
What is the derivative of
f
(
x
)
=
cos
(
x
)
f(x) = \text{cos}(x)
f
(
x
)
=
cos
(
x
)
?
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ANSWER
−
sin
(
x
)
-\text{sin}(x)
−
sin
(
x
)
. Derivative of cosine is negative sine.
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