deletions | additions       diff --git a/vec_x_t_Delta_t__3.tex b/vec_x_t_Delta_t__3.tex  index 468c213..283f7f6 100644  --- a/vec_x_t_Delta_t__3.tex  +++ b/vec_x_t_Delta_t__3.tex 
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$$\vec{x}(t + \Delta t) = \vec{x}(t) + 2  \vec{x}(t) - \vec{x}(t-\Delta t) + \vec{a}(t) \Delta t^2  - \frac{1}{12} \vec{b}(t-\Delta (\vec{b}(t-\Delta  t)\Delta t^3  - \frac{1}{12} \vec{b}(t) \vec{b}(t))  \Delta t^3 +\vec{a}(t) \Delta t^2 +  O(\Delta t^4) $$