Chapter 13.2, Problem 4E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

(a) Sketch the plane curve with the given vector equation.

(b) Find **r***'*(*t*).

(c) Sketch the position vector **r**(*t*) and the tangent vector **r***'*(*t*) for the given value of *t*.

**4. r**(*t*) = ⟨*t*^{2}, *t*^{3}⟩, *t* = 1

**(a)**

To determine

**To sketch:** The plane curve with the vector equation

Explanation

Write the *x*-component of the vector

Rearrange the expression

Write the *y*-component of the vector

Substitute

Modify the expression as follows.

The required curve is a graph of

Find the vector

**(b)**

To determine

**To find:** The vector

**(c)**

To determine

**To sketch:** The position vector

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