Practice: Vector Functions

8 multiple choice · 4 free response · 1 walkthroughs

Q1.

basic

The domain of

r (t) = ⟨ ln t, 1 - t, \frac{1}{t} ⟩

Q2.

basic

The curve

r (t) = ⟨ 2 cos t, 3 sin t, 0 ⟩

Q3.

basic

lim_{t \to 0} ⟨ \frac{s i n t}{t}, e^{t}, cos t ⟩ =

Q4.

basic

Parameterize the line segment from

(1, 0, 0)

(0, 1, 1)

0 \leq t \leq 1

Q5.

basic

The projection of

r (t) = ⟨ t, t^{2}, t^{3} ⟩

onto the

x y

-plane is

Q6.

intermediateFinal Review #34 style

Where does

r (t) = ⟨ 2 - t^{3}, 2 t - 1, ln t ⟩

intersect the

x z

-plane?

Q7.

intermediate

The curve where the surfaces

z = x^{2} + y^{2}

and

z = 4

intersect can be parameterized by

Q8.

basicFinal Review T/F

True/False: The curve

r (t) = ⟨ cos t, sin t, t ⟩

is a circle.