Parametric Functions and Rates of Change
AP Precalculus · Flashcards · Recall
AP PRECALCULUS · FLASHCARDS
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QUESTION
State the parametric equations for a line with slope
m
m
m
passing through
(
x
0
,
y
0
)
(x_0, y_0)
(
x
0
,
y
0
)
.
QUESTION
What is the second derivative
d
2
y
d
x
2
\frac{d^2y}{dx^2}
d
x
2
d
2
y
for parametric equations?
QUESTION
What is the rate of change of arc length in parametric form?
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ANSWER
d
s
d
t
=
(
(
d
x
d
t
)
2
+
(
d
y
d
t
)
2
)
\frac{ds}{dt} = \sqrt{((\frac{dx}{dt})^2 + (\frac{dy}{dt})^2)}
d
t
d
s
=
((
d
t
d
x
)
2
+
(
d
t
d
y
)
2
)
. Magnitude of velocity vector gives speed of arc traversal.
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