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Putnam 1958 November B4

Source: Putnam 1958 November

July 19, 2022
Putnamfunctionderivativelimit

Problem Statement

Let CC be a real number, and let f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} be a three times differentiable function such that lim⁡x→∞f(x)=C,      lim⁡x→∞f′′′(x)=0. \lim_{x \to \infty} f(x)=C, \;\; \; \lim_{x \to \infty} f'''(x)=0. Prove that lim⁡x→∞f′(x)=0    and    lim⁡x→∞f′′(x)=0. \lim_{x \to \infty} f'(x) =0 \;\; \text{and} \;\; \lim_{x \to \infty} f''(x)=0.
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