Defining and Differentiating Vector-Valued Functions
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
State the formula for the arc length of a curve
r
(
t
)
\text{r}(t)
r
(
t
)
from
a
a
a
to
b
b
b
.
QUESTION
Calculate the unit tangent vector for
r
(
t
)
=
(
3
t
4
t
)
\text{r}(t) = \begin{pmatrix} 3t \\ 4t \end{pmatrix}
r
(
t
)
=
(
3
t
4
t
)
.
QUESTION
Calculate the speed for
r
(
t
)
=
(
sin
(
t
)
cos
(
t
)
)
\text{r}(t) = \begin{pmatrix} \text{sin}(t) \\ \text{cos}(t) \end{pmatrix}
r
(
t
)
=
(
sin
(
t
)
cos
(
t
)
)
.
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ANSWER
Speed is 1.
∣
v
(
t
)
∣
=
cos
2
(
t
)
+
sin
2
(
t
)
=
1
|\text{v}(t)| = \sqrt{\cos^2(t) + \sin^2(t)} = 1
∣
v
(
t
)
∣
=
cos
2
(
t
)
+
sin
2
(
t
)
=
1
.
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