deletions | additions       diff --git a/vec_x_t_Delta_t__3.tex b/vec_x_t_Delta_t__3.tex  index 283f7f6..eee0e42 100644  --- a/vec_x_t_Delta_t__3.tex  +++ b/vec_x_t_Delta_t__3.tex 
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$$\vec{x}(t + \Delta t) = 2 \vec{x}(t) - \vec{x}(t-\Delta t) + \vec{a}(t) \Delta t^2 - \frac{1}{12} (\vec{b}(t-\Delta t) - +  \vec{b}(t)) \Delta t^3 + O(\Delta t^4) $$