Describe in words the curve represented by the parametric

Question

Question: Describe in words the curve represented by the parametric equations

x = 3 + t³, y = 5 - t³

(a) Sketch the parameterized curve x = t cos t, y = t sin t for 0 ≤ t ≤ 4π.

(b) By calculating the position at t = 2 and t = 2.01, estimate the speed at t = 2.

(c) Use derivatives to calculate the speed at t = 2 and compare your answer to part (b).