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Consider the sequence \((u_n)\) defined for \(n \ge 4\) by \(u_n=\dfrac{n^2+1}{n-3}\).
  1. Show that using the quotient rule directly leads to an indeterminate form.
  2. Show that for all \(n \ge 4\), \(u_n=\dfrac{n\left(1+\frac{1}{n^2}\right)}{1-\frac{3}{n}}\).
  3. Deduce the limit of the sequence \((u_n)\).

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