Mathematics

Mathematics

Problem

Make a large sketch of the curve described by the vector function r(t)=⟨t2,t⟩\mathbf{r}(t) = \langle t^2, t \rangle , 0≤t≤20 \le t \le 2 , and draw the vectors r(1)\mathbf{r}(1) , r(1.1)\mathbf{r}(1.1) , and r(1.1)−r(1)\mathbf{r}(1.1) - \mathbf{r}(1). a. Draw the vector r′(1)\mathbf{r}'(1) starting at (1,1)(1, 1) , and compare it with the vector r(1.1)−r(1)0.1\frac{\mathbf{r}(1.1) - \mathbf{r}(1)}{0.1} Explain why these vectors are so close to each other in length and direction.

Browse the problem library