Q: Sketch the curve with the given vector equation. Indicate with an
Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases. r(t) = cos t i - cos t j + sin t k
See AnswerQ: Use Formula 11 to find the curvature. y = tan
Use Formula 11 to find the curvature. y = tan x
See AnswerQ: Use Formula 11 to find the curvature. y = xex
Use Formula 11 to find the curvature. y = xex
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 = ex
See AnswerQ: Find an equation of a parabola that has curvature 4 at the
Find an equation of a parabola that has curvature 4 at the origin.
See AnswerQ: Show that if r is a vector function such that r'' exists
Show that if r is a vector function such that r'' exists, then
See AnswerQ: If a curve has the property that the position vector r(
If a curve has the property that the position vector r(t) is always perpendicular to the tangent vector r'(t), show that the curve lies on a sphere with center the origin.
See AnswerQ: If u(t) = r(t) ∙ [
If u(t) = r(t) ∙ [r'(t) × r''(t)], show that u'(t) – r(t) ∙ [r'(t) × r'''(t)]
See AnswerQ: Use a graphing calculator or computer to graph both the curve and
Use a graphing calculator or computer to graph both the curve and its curvature function k (x) on the same screen. Is the graph of what you would expect? y = x4 - 2x2
See AnswerQ: Use a graphing calculator or computer to graph both the curve and
Use a graphing calculator or computer to graph both the curve and its curvature function k (x) on the same screen. Is the graph of what you would expect? y = x-2
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