Question

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

Answer 1

Solution :

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

= [ 1 + ( 1 - 1 )² ]/[ 1 + 1² ]

= 1/2

Therefore ,

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

= 1/2

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