\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider the function \(f(x) = \dfrac{x}{(x-1)^2}\).
  1. Evaluate the one-sided limits of \(f(x)\) as \(x\) approaches 1:
    • \(\displaystyle\lim_{x \to 1^+} f(x)\)
    • \(\displaystyle\lim_{x \to 1^-} f(x)\)
  2. Does \(\displaystyle\lim_{x \to 1} f(x)\) exist? Justify your answer.
  3. Hence, state the equation of any vertical asymptotes of the graph of \(y=f(x)\).

Capture an image of your work. AI teacher feedback takes approximately 10 seconds.