Find if and .

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Find

\mathbf{r}(t)

\mathbf{r}'(t) = t \mathbf{i} + e^t \mathbf{j} + te^t \mathbf{k}

and

\mathbf{r}(0) = \mathbf{i} + \mathbf{j} + \mathbf{k}