A photographer takes a picture of a three-foot painting hanging in an art gallery. The
Chapter 5, Problem 100(choose chapter or problem)
A photographer takes a picture of a three-foot painting hanging in an art gallery. The camera lens is 1 foot below the lower edge of the painting (see figure). The angle \(\beta\) subtended by the camera lens x feet from the painting is \(\beta = \arctan[3x/(x^2+4)], x > 0\).
(a) Use a graphing utility to graph \(\beta\) as a function of x.
(b) Use the trace feature to approximate the distance from the picture when \(\beta\) is maximum.
(c) Identify the asymptote of the graph and discuss its meaning in the context of the problem.
Text Transcription:
beta
beta = arctan[3x/(x^2+4)], x > 0
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