Q: Find r (t) if r' (t) = t
Find r (t) if r' (t) = t i + e' t j + te' k and r (0) = i + j + k.
See AnswerQ: Show that the tangent vector to a curve defined by a vector
Show that the tangent vector to a curve defined by a vector function r(t) points in the direction of increasing t. [Hint: Refer to Figure 1 and consider the cases h > 0 and h Figure 1:
See AnswerQ: Reparametrize the curve / with respect to arc
Reparametrize the curve with respect to arc length measured from the point (1, 0) in the direction of increasing t. Express the reparametrization in its simplest form. What can you conclude about th...
See AnswerQ: Graph the curve with parametric equations x = cos t, y
Graph the curve with parametric equations x = cos t, y = sin t, z = sin 5t and find the curvature at the point (1, 0, 0).
See AnswerQ: Find the curvature and torsion of the curve x = sin h
Find the curvature and torsion of the curve x = sin h t, y = cos h t, z = t at the point (0, 1, 0).
See AnswerQ: The DNA molecule has the shape of a double helix (see
The DNA molecule has the shape of a double helix (see Figure 3 on page 850). The radius of each helix is about 10 angstroms (1 Ã… = 10-8 cm). Each helix rises about 34 Ã… durin...
See AnswerQ: Let’s consider the problem of designing a railroad track to make a
Let’s consider the problem of designing a railroad track to make a smooth transition between sections of straight track. Existing track along the negative x-axis is to be joined smoo...
See AnswerQ: At what point does the curve have maximum curvature? What happens
At what point does the curve have maximum curvature? What happens to the curvature as x →∞ ? y = ln x
See AnswerQ: (a). Is the curvature of the curve C shown in
(a). Is the curvature of the curve C shown in the figure greater at P or at Q? Explain. (b). Estimate the curvature at P and at Q by sketching the osculating circles at those points.
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