The \( \mathrm{L}^2 \) norm of the difference between \( f \) and \( p \) is given by:
\[ \|f - p\|_2 = \left(\int_0^1 (f(t) - p(t))^2 \, dt\right)^{1/2} \]
The goal is to minimize this norm.
Step 2: Set up the minimization problem
To find the best approximation,
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