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The Eiffel Tower property Let R be the region between the curves y = e−cx and y = −e−cx on the interval [a, ∞), where a ≥ 0 and c > 0. The center of mass of R is located at
- a. For a = 0 and c = 2, sketch the curves that define R and find the center of mass of R. Indicate the location of the center of mass.
- b. With a = 0 and c = 2, find equations of the lines tangent to the curves at the points corresponding to x = 0.
- c. Show that the tangent lines intersect at the center of mass.
- d. Show that this same property holds for any a ≥ 0 and any c > 0; that is, the tangent lines to the curves y = ± e−cx at x = a intersect at the center of mass of R.
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