Ononot — Let fn(x) = \frac{x^n}{1+x^n} for x \in [0, 2]. Define f(x)

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Limits & Continuityhard

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Let $f_n(x) = \frac{x^n}{1+x^n}$ for $x \in [0, 2]$ . Define $f(x) = \lim_{n \to \infty} f_n(x)$ . Which of the following accurately describes the convergence and the nature of the limit function $f(x)$ ?