Find the derivative of mathbfr(t) = t2mathbfi - te-tmathbfj + sin(2t)m | Mathematics I 2079

Mathematics I20795 marksNumerical: vector derivative tangentDerivative and integrals of vector functions

Find the derivative of $\mathbf{r}(t) = t^2\mathbf{i} - te^{-t}\mathbf{j} + \sin(2t)\mathbf{k}$ and find the unit tangent vector at $t = 0$ . [5]

Find the derivative of $\mathbf{r}(t) = t^2\mathbf{i} - te^{-t}\mathbf{j} + \sin(2t)\mathbf{k}$ and find the unit tangent vector at $t = 0$. [5]

Vector function: $\mathbf{r}(t) = t^2\,\mathbf{i} - te^{-t}\,\mathbf{j} + \sin(2t)\,\mathbf{k}$ Point of evaluation: $t = 0$ Required: (a) $\mathbf{r}'(t)$ , (b) unit tangent vector $\mathbf{T}(0)$ . All data present. --- i-component: $\dfrac{d}{dt}(t^2) = 2t$ j-component:

Vector function: $$\mathbf{r}(t) = t^2,\mathbf{i} - te^{-t},\mathbf{j} + \sin(2t),\mathbf{k}$$ Point of evaluation: $t = 0$ Required: (a) $\mathbf{r}'(t)$, (b) unit tangent vector $\mathbf{T}(0)$. All data present. --- i-component: $\dfrac{d}{dt}(t^2) = 2t$ j-component:

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Find the derivative of mathbfr(t) = t2mathbfi - te-tmathbfj + sin(2t)mathbfk and find the unit tangent vector at t = 0.