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Consider the sequence \((u_n)\) defined by \(u_{n+1} = \dfrac{u_n^2 + 1}{2}\).We assume that \((u_n)\) converges to a real number \(\ell\).The graph of \(f(x) = \dfrac{x^2 + 1}{2}\) and the line \(y = x\) are shown below:
  1. Graphically identify the point where the curve and the line intersect. What is the potential limit \(\ell\)?
  2. Algebraically solve the equation \(f(x) = x\) to confirm the value of \(\ell\).

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