Question

why do we need to assume that the curve c is traversed exactly once by the vector-valued function as t increases from t

Answer 1

It is important to note that assuming a one-to-one traversal of the curve is not always necessary or applicable in all situations. Some vector-valued functions may traverse a curve multiple times or skip certain portions altogether. In such cases, the assumption may need to be revised or alternative approaches may be required to accurately describe and analyze the behavior of the function along the curve.

Explanation: