AP Calculus BC Quiz
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PARAMETRIC, POLAR, AND VECTOR FUNCTIONS
Question 1
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A swimmer's position is
r
(
t
)
=
⟨
cos
(
3
t
)
,
sin
(
3
t
)
,
t
2
⟩
\mathbf{r}(t)=\langle \cos(3t),\ \sin(3t),\ t^2\rangle
r
(
t
)
=
⟨
cos
(
3
t
)
,
sin
(
3
t
)
,
t
2
⟩
. What is
r
′
(
t
)
\mathbf{r}'(t)
r
′
(
t
)
?
A
⟨
−
sin
(
3
t
)
,
cos
(
3
t
)
,
2
t
⟩
\langle -\sin(3t),\ \cos(3t),\ 2t\rangle
⟨
−
sin
(
3
t
)
,
cos
(
3
t
)
,
2
t
⟩
B
⟨
−
3
sin
(
3
t
)
,
3
cos
(
3
t
)
,
2
t
⟩
\langle -3\sin(3t),\ 3\cos(3t),\ 2t\rangle
⟨
−
3
sin
(
3
t
)
,
3
cos
(
3
t
)
,
2
t
⟩
C
⟨
3
sin
(
3
t
)
,
−
3
cos
(
3
t
)
,
2
t
⟩
\langle 3\sin(3t),\ -3\cos(3t),\ 2t\rangle
⟨
3
sin
(
3
t
)
,
−
3
cos
(
3
t
)
,
2
t
⟩
D
⟨
−
3
sin
(
3
t
)
,
3
cos
(
3
t
)
,
t
2
⟩
\langle -3\sin(3t),\ 3\cos(3t),\ t^2\rangle
⟨
−
3
sin
(
3
t
)
,
3
cos
(
3
t
)
,
t
2
⟩
E
⟨
−
3
cos
(
3
t
)
,
3
sin
(
3
t
)
,
2
t
⟩
\langle -3\cos(3t),\ 3\sin(3t),\ 2t\rangle
⟨
−
3
cos
(
3
t
)
,
3
sin
(
3
t
)
,
2
t
⟩
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