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Chapter 11: Q. 37 (page 860)
Evaluate and simplify the indicated quantities in Exercises 35–41.
The simplification of is .
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As we saw in Example 1, the graph of the vector-valued function is a circular helix that spirals counterclockwise around the z-axis and climbs ast increases. Find another parametrization for this helix so that the motion along the helix is faster for a given change in the parameter.
Let be a vector-valued function defined on an open interval containing the point . Prove that r(t) is continuous at if and only if and are both continuous at .
Let y = f(x). State the definition for the continuity of the function f at a point c in the domain of f .
Evaluate the limits in Exercises 42–45.
Given a twice-differentiable vector-valued function , why does the principal unit normal vector point into the curve?
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