Evaluate the following limit: _ x 1 1+(x-1)^2 1+ x^2 - Vidyadip

Question

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow1}\frac{1+(\text{x}-1)^2}{1+{\text{x}^2}}$

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Answer

$\lim\limits_{\text{x}\rightarrow1}\frac{1+({\text{x}}-1)}{1+{\text{x}^2}}=\frac{1+0^2}{1+1}=\frac{1}{2}$

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