lim _ x→ 1 1+( x 1 ) #160; ^ 2 1+ x ^ 2 #160; =lim _ x→ 1 1+( 1 1 ) #160; ^ 2 1+ 1 ^ 2 #160; =lim _ x→ 1 1 2 #160; = 1 2 ...

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Algebra of Limits

limx → 11+x-1...

Question

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

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Solution

${lim}_{x \to 1} \frac{1 + {(x - 1)}^{2}}{1 + x^{2}} = {lim}_{x \to 1} \frac{1 + {(1 - 1)}^{2}}{1 + 1^{2}} = {lim}_{x \to 1} \frac{1}{2} = \frac{1}{2}$

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