3-8 (a) Sketch the plane curve with the given vector equation. (b) Find r'(t). (c) Sketch the position vector r(t) and the tangent vector r'(t) for the given value of t. 3. r(t) = (t – 2, t² + 1), 4....

Problem #6

a) Sketch the plane curve with the given vector equation.

(b) Find r'(t).

c) Sketch the position vector r(t) and the tangent vector r'(t) for the given value of t.

Extracted text: 3-8 (a) Sketch the plane curve with the given vector equation. (b) Find r'(t). (c) Sketch the position vector r(t) and the tangent vector r'(t) for the given value of t. 3. r(t) = (t – 2, t² + 1), 4. r(t) = (1 + t, yF), 1= 1 5. r(t) = sin t i + 2 cos tj, t= T/4 %3| 6) r(t) — е'i +e"j, t— 0 3t 7. r(t) = e'i + eªj, t= 0 8. r(t) = (1 + cos t) i + (2 + sin t) j, t = T/6