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Section 6 Wrap Up Questions

  1. Are the following statements true or false? Give reasons for your answers.

    1. A simple-closed curve is both simple and closed.

    2. It is possible to find two different parameterizations for a curve \(C\text{,}\) one of which is differentiable and one which is not differentiable.

    3. If a curve \(C\) parameterized by \(\vec{r}(t)\) is differentiable, then it is continuous.

  2. Explain how to determine algebraically if a curve is closed. Explain how to determine geometrically if a curve is closed.

  3. Explain how to determine algebraically if a curve is simple. Explain how to determine geometrically if a curve is simple.

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