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Consider the function \(f(x) = \dfrac{\sqrt{9x^2+4}}{x-1}\).
  1. Find \(\displaystyle\lim_{x \to \infty} f(x)\).
  2. Find \(\displaystyle\lim_{x \to -\infty} f(x)\).
  3. Hence, write down the equations of any horizontal asymptotes of the graph of \(y=f(x)\).

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