Chapter 11: Q. 2 (page 901)
Sketching vector functions: Sketch the following vector functions.
x=cos x, y=x
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Evaluate and simplify the indicated quantities in Exercises 35–41.
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.
Let y = f(x). State the definition for the continuity of the function f at a point c in the domain of f .
Under what conditions does a differentiable vector-valued functionr(t) not have a unit tangent vector at a point in the domain of r(t)?
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.
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