$\lim_{x \to 1} \frac{1 + {(x - 1)}^{2}}{1 + x^{2}}$

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Solution

$\lim_{x \to 1} [\frac{1 + {(x - 1)}^{2}}{1 + x^{2}}] = \frac{1 + {(1 - 1)}^{2}}{1 + 1^{2}} = \frac{1}{2}$

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