Ononot — Consider the sequence of functions fn(x) = \frac{n x^2}{1 +

Limits & Continuityhard

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Consider the sequence of functions $f_n(x) = \frac{n x^2}{1 + n x}$ for $x \geq 0$ . Evaluate the limit $L(x) = \lim_{n \to \infty} f_n(x)$ and determine if the convergence is uniform on $[0, 1]$ .