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Limits & Continuityhard
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Consider the sequence of functions fn(x)=nx21+nxf_n(x) = \frac{n x^2}{1 + n x}fn​(x)=1+nxnx2​ for x≥0x \geq 0x≥0. Evaluate the limit L(x)=lim⁡n→∞fn(x)L(x) = \lim_{n \to \infty} f_n(x)L(x)=limn→∞​fn​(x) and determine if the convergence is uniform on [0,1][0, 1][0,1].