# Solución

Usa la ecuación 3.5: $$\begin{aligned} \bold{r'}(t) &= \lim\limits_{\Delta t \to 0}\frac{\bold{r}(t+\Delta t)-\bold{r}(t)}{\Delta t}\\ &= \lim\limits_{\Delta t \to 0}\frac{[(3(t+\Delta t)+4)\bold{i} + ((t+\Delta t)^2−4(t+\Delta t)+3)\bold{j}]−[(3t+4)\bold{i}+(t^2−4t+3)\bold{j}]}{\Delta t}\\ &= \lim\limits_{\Delta t \to 0}\frac{(3\Delta t)\bold{i}+(2t\Delta t +(\Delta t)^2−4\Delta t)\bold{j}}{\Delta t}\\ &= \lim\limits_{\Delta t \to 0}(3\bold{i}+(2t+\Delta t−4)\bold{j})\\ &= 3\bold{i}+(2t−4)\bold{j} \end{aligned}$$