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$f(x)$ is a differentiable function on the real line such that $\underset{x \to \infty=}{\lim} f(x) =1$ and $\underset{x \to \infty=}{\lim} f’(x) =\alpha$. Then

  1. $\alpha$ must be $0$
  2. $\alpha$ need not be $0$, but $\mid \alpha \mid <1$
  3. $\alpha >1$
  4. $\alpha < -1$
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A seems to be the most appropriate answer.
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