**Problem : **
Consider the parametric curve (*x*(*t*), *y*(*t*)) = (2*t*, sin(*t*)). What function has a graph that
coincides with this curve?

**Problem : **
What is the velocity vector of the parametric curve (2*t*, sin(*t*)) at time *t* = 0? *Π*/2?
*Π*?

(x'(0), y'(0)) | = | (2, 1) | |

(x'(Π/2), y'(Π/2)) | = | (2, 0) | |

(x'(Π), y'(Π)) | = | (2, - 1) |

**Problem : **
What is the velocity vector at time *t* = 2*Πk* (*k*≥ 0 an integer)
of the spiral (*t* cos(*t*), *t* sin(*t*))? Suppose a particle is tracing
out the spiral, so that it is at the point (*t* cos(*t*), *t* sin(*t*)) at
time *t*. How fast is the particle moving at time *t*?

(x'(2Πk), y'(2Πk)) = (1, 2Πk) |

The speed of the particle at time

= |

This makes sense because the speed of the particle must continue to rise if it is to continue to complete larger and larger turns of the spiral in the same amount of time (2

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