Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 782

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\[1)\ s(t) = \frac{3}{2}t^{2}\]

\[\mathrm{\Delta}s = \frac{f(t + h) - f(t)}{h} =\]

\[= \frac{\frac{3}{2}(t + h)^{2} - \frac{3}{2}t^{2}}{h} =\]

\[= \frac{\frac{3}{2}t^{2} + 3th + \frac{3}{2}h^{2} - \frac{3}{2}t^{2}}{h} =\]

\[= \frac{3th - \frac{3}{2}h^{2}}{h} = 3t - \frac{3}{2}h\]

\[v = \lim_{h \rightarrow 0}\left( 3t - \frac{3}{2}h \right) =\]

\[= 3t - \frac{3}{2} \bullet 0 = 3t.\]

\[Ответ:\ \ 3t.\]

\[2)\ s(t) = 5t^{2}\]

\[\mathrm{\Delta}s = \frac{f(t + h) - f(t)}{h} =\]

\[= \frac{5(t + h)^{2} - 5t^{2}}{h} =\]

\[= \frac{5t^{2} + 10th + 5h^{2} - 5t^{2}}{h} =\]

\[= \frac{10th + 5h^{2}}{h} = 10t + 5h\]

\[v = \lim_{h \rightarrow 0}(10t + 5h) =\]

\[= 10t + 5 \bullet 0 = 10t.\]

\[Ответ:\ \ 10t.\]