Calculus 2 Quiz
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PARAMETRIC, POLAR & VECTOR FUNCTIONS
Question 1
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Let
r
(
t
)
=
⟨
t
+
1
,
t
2
,
1
⟩
\mathbf{r}(t) = \langle t+1, t^2, 1 \rangle
r
(
t
)
=
⟨
t
+
1
,
t
2
,
1
⟩
and
s
(
t
)
=
⟨
t
+
1
,
sin
t
,
cos
t
⟩
\mathbf{s}(t) = \langle t+1, \sin t, \cos t \rangle
s
(
t
)
=
⟨
t
+
1
,
sin
t
,
cos
t
⟩
. Find the derivative
d
d
t
[
r
(
t
)
×
s
(
t
)
]
\frac{d}{dt}[\mathbf{r}(t) \times \mathbf{s}(t)]
d
t
d
[
r
(
t
)
×
s
(
t
)]
at
t
=
0
t=0
t
=
0
.
A
⟨
−
1
,
0
,
1
⟩
\langle -1, 0, 1 \rangle
⟨
−
1
,
0
,
1
⟩
B
⟨
0
,
−
1
,
0
⟩
\langle 0, -1, 0 \rangle
⟨
0
,
−
1
,
0
⟩
C
⟨
−
1
,
1
,
1
⟩
\langle -1, 1, 1 \rangle
⟨
−
1
,
1
,
1
⟩
D
⟨
1
,
0
,
−
1
⟩
\langle 1, 0, -1 \rangle
⟨
1
,
0
,
−
1
⟩
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