[tex] a\equiv\dfrac{\Delta v}{\Delta t} [/tex]
Pentru un interval foarte mic de timp [tex]\Delta t[/tex]:
[tex] a=\dfrac{v(t+\Delta t)-v(t)}{\Delta t}=\dfrac{9(t+\Delta t)^4+7(t+\Delta t)+2-9t^4-7t-2}{\Delta t} [/tex]
[tex] a=\dfrac{\Delta t(36 t^3 + 54 t^2 \Delta t+ 36 t (\Delta t)^2 + 9 (\Delta t)^3 + 7)}{\Delta t}\\a= 36 t^3 + 54 t^2 \Delta t+ 36 t (\Delta t)^2 + 9 (\Delta t)^3 + 7\approx 36t^3+7\:(\Delta t\to 0) [/tex]
Poti verifica imediat acest lucru prin a deriva functia v(t). In rezolvare am folosit formula [tex] (a+b)^4= a^4 + 4 a^3 b + 6 a^2 b^2 + 4 a b^3 + b^4 [/tex] si faptul ca [tex] \Delta t [/tex] e ales neglijabil fata de [tex] t [/tex].
