← Calculus of Vector Functions & Arc Length

Practice: Vector Calculus

8 multiple choice · 4 free response · 1 walkthroughs

Q1.

basic

\frac{d}{d t} ⟨ t^{2}, e^{t}, sin t ⟩ =

Q2.

intermediate

If

r^{''} (t) = ⟨ 0, 0, - g ⟩

and

r^{'} (0) = ⟨ v_{0}, 0, 0 ⟩

,

r (0) = 0

, then

r (t) =

Q3.

basic

The unit tangent vector to

r (t) = ⟨ cos t, sin t, 0 ⟩

at

t = π /2

is

Q4.

intermediate

Arc length of

r (t) = ⟨ 3 cos t, 3 sin t, 4 t ⟩

from

t = 0

to

t = 2 π

is

Q5.

intermediateFinal Review #41

Is

r (t) = ⟨ cos t / 2, cos t / 2, sin t ⟩

parameterized by arc length?

Q6.

basic

\frac{d}{d t} (u (t) \cdot v (t)) =

Q7.

intermediate

If

∣ r (t) ∣

is constant, then

r

and

r^{'}

are

Q8.

basic

Evaluate

\int_{0}^{1} ⟨ 2 t, 3 t^{2}, 1 ⟩ d t

.