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Consider the function \(f(x) = \dfrac{x+1}{x-2}\).
  1. Evaluate the one-sided limits of \(f(x)\) as \(x\) approaches 2:
    • \(\displaystyle\lim_{x \to 2^+} f(x)\)
    • \(\displaystyle\lim_{x \to 2^-} f(x)\)
  2. Does \(\displaystyle\lim_{x \to 2} f(x)\) exist? Justify your answer.
  3. Hence, state the equation of any vertical asymptotes of the graph of \(y=f(x)\).

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