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 where (The profile of the Eiffel Tower is modeled by the two exponential curves; see the Guided Project The exponential Eiffel Tower.)

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.

Transcribed Image Text:

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