13.1 Vector Functions and Space Curves PDF

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MATH 2D 13.1 Vector Functions and Space Curves Morgan Holve Learning Goals: Students will calculate points and surfaces of intersecting equations. Students will recognize vector functions by matching graphs to their equations. Lecture Review: 1. What form does a vector-valued function take?

How does one find the limit of a vector function?

What is the general, parametric form for a space curve?

Limits: 2. Find the limit: a. lim e−3t i + t→0

b. lim ≺ t→∞

1+t2 , 1−t2

t2 sin2 t j

+ cos(2t)k

tan−1 (t),

1−e−2t t

≻

Space Curves: 3. Find the vector function that represents the intersection between the hyperbolic paraboloid z = x2 − y2 and the cylinder x2 + y2 = 1

4. The trajectories of two particles are modeled by the vector functions r 1 (t) =≺ t2 , 7t − 12, t2 ≻ r 2 (t) =≺ 2t − 3, t2 , 5t − 6 ≻ Do these particles collide? If so, where and when?

5. Match the parametric equations with the corresponding graph

Independent Practice: 6. Determine if the vectors a =≺ 3,− 1, 3 ≻ and b =≺ 3, 3,− 2 ≻ are orthogonal, parallel or neither.

7. Find the Cartesian equation of y = √3x...