deletions | additions       diff --git a/Or_frac_vec_x_t__.tex b/Or_frac_vec_x_t__.tex  index 90601b0..b90f5c8 100644  --- a/Or_frac_vec_x_t__.tex  +++ b/Or_frac_vec_x_t__.tex 
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$$ \frac{\vec{x}(t+2\Delta t) - \vec{x}(t)}{2 \Delta t} - \frac{\vec{x}(t+\Delta t) - \vec{x}(t-\Delta t)}{2 \Delta t} = \frac{\vec{a}(t) + \vec{a}(t + \Delta t)}{2} \Delta t $$  $$ (\vec{x}(t+2\Delta \vec{x}(t+2\Delta  t) - \vec{x}(t)) \vec{x}(t)  - (\vec{x}(t+\Delta \vec{x}(t+\Delta  t) - +  \vec{x}(t-\Delta t)) t)  = (\vec{a}(t) + \vec{a}(t + \Delta t)) \Delta t^2 $$