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Mathematics
Mathematics
Problem
Let
r
(
t
)
=
⟨
t
,
t
2
,
2
t
⟩
\mathbf r(t)=\langle t,\, t^{2},\,2t\rangle
r
(
t
)
=
⟨
t
,
t
2
,
2
t
⟩
for
t
≥
0
t\ge 0
t
≥
0
. (a) Compute
r
′
(
t
)
\mathbf r'(t)
r
′
(
t
)
and evaluate
r
′
(
1
)
\mathbf r'(1)
r
′
(
1
)
. (b) Find the unit tangent vector to the curve at
t
=
1
t=1
t
=
1
. (c) Determine the curvature of the curve at
t
=
1
t=1
t
=
1
.
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