This is about the particle pullout rate. (a) Demonstrate that x (t) x (t + 3t) 3x (t + 2t) + 3x (t +

This is about the particle pullout rate.

(a) Demonstrate that x (t) ≈ x (t + 3Δt) −3x (t + 2Δt) + 3x (t + Δt) −x (t) all divided byΔt3.

(b) If we have an uncertainty Δx in the measure of the position, even if we assume a measure perfectly need in time, what will be the uncertainty in the start-up rate? Generalize your result to the n-th derivative.