deletions | additions       diff --git a/vec_x_t_Delta_t__3.tex b/vec_x_t_Delta_t__3.tex  index a27e8ad..468c213 100644  --- a/vec_x_t_Delta_t__3.tex  +++ b/vec_x_t_Delta_t__3.tex 
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$$\vec{x}(t + \Delta t) = \vec{x}(t) + \vec{x}(t) - \vec{x}(t-\Delta t) - \frac{1}{6} \vec{b}(t-\Delta t) \Delta t^3 + \frac{1}{4} \frac{1}{12}  \vec{b}(t-\Delta t) \Delta t^3 - \frac{1}{12} \vec{b}(t) \Delta t^3 + \vec{a}(t) \Delta t^2 + O(\Delta t^4) $$