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A condition for boundedness

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October 31, 2019
functionreal analysis

Problem Statement

Let be a continuous function f:R≥0⟶R f:\mathbb{R}_{\ge 0}\longrightarrow\mathbb{R} that has a root, and for which the line y=0 y=0 in the Cartesian plane is an horizontal asymptote. Show that f f is bounded and touches its boundaries.
Mihai Piticari and Vladimir Cerbu
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