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Chapter 11: Q. 41 (page 860)
Evaluate and simplify the indicated quantities in Exercises 35鈥�41.
The simplification of is .
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Every description of the DNA molecule says that the strands of the helices run in opposite directions. This is meant as a statement about chemistry, not about the geometric shape of the double helix. Consider two helices
(a) Sketch these two helices in the same coordinate system, and show that they run geometrically in different directions.
(b) Explain why it is impossible for these two helices to fail to intersect, and hence why they could not form a configuration for DNA.
Let y = f (x). State the definition for the continuity of the function f at a point c in the domain of f .
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 whose graph is a curve C, and let be the acceleration vector. Prove that if is always zero, then C is a straight line.
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.
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