Chapter 11: Q. 40 (page 872)
Evaluate the integrals in Exercises 40–44.
The value for the given vector function is.
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Prove that if a particle moves along a curve at a constant speed, then the velocity and acceleration vectors are orthogonal.
Find parametric equations for each of the vector-valued functions in Exercises 26–34, and sketch the graphs of the functions, indicating the direction for increasing values of t.
If , , and are nonzero constants, the graph of a vector function of the formrole="math" localid="1649577570077" is called a twisted cubic. Prove that a twisted cubic intersects any plane in at most three points.
For each of the vector-valued functions in Exercises ,find the unit tangent vector and the principal unit normal vector at the specified value of t.
Show that the graph of the vector function is a circle. (Hint: Show that the graph lies on a sphere and in a plane.)
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