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Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t...

Question:

Sketch the curve with the given vector equation. Indicate with an arrow the direction in which {eq}t {/eq} increases.

{eq}\displaystyle\; \mathbf{r}(t) = \left\langle t^{2} - 1, \;t \right\rangle {/eq}

Sketch of Parametric Equation:

Let us consider a parametric curve in the plane described by the vector function

{eq}\mathbf r(t) = x(t) \mathbf i + y(t) \mathbf j. {/eq}

A sketch of the curve can be produced by plotting the sequence of points (x,y) when the parameter t varies.

Answer and Explanation:

Consider the parametric curve described by the vector function

{eq}\displaystyle\; \mathbf{r}(t) = \left\langle t^{2} - 1, \;t \right\rangle {/eq}

A sketch the curve when the parameter t varies in the range {eq}t \in [-2,2] {/eq} is reported in the figure below

together with an arrow indicating the direction where t increases.

curve


Learn more about this topic:

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Graphs of Parametric Equations

from Precalculus: High School

Chapter 24 / Lesson 5
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