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Question
\[\lim_{x \to 1} \frac{1 + \left( x - 1 \right)^2}{1 + x^2}\]
Solution
\[\lim_{x \to 1} \left[ \frac{1 + \left( x - 1 \right)^2}{1 + x^2} \right]\]
\[ = \frac{1 + \left( 1 - 1 \right)^2}{1 + 1^2}\]
\[ = \frac{1}{2}\]
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