Question

$1 + (x - 1) {?}^{2} { \div }1 + x {?}^{2}$

Answer 1

(iv)
$since \: no \: indeterminate \: form \: occured \: so \: we \: can \: put \: limiting \: value \: 3 \\ \frac{ \sqrt{x + 8} }{ \sqrt{x} } \\ = \frac{ \sqrt{11} }{ \sqrt{3} } \\ = \sqrt{ \frac{11}{3} } ans$
(vi)
here too indeterminate form is not formed so we can directly put limiting value.

$\frac{1 + ({1 - x)}^{2} }{1 + {x}^{2} } \\ put \: x = 1 \\ \frac{1 + 0}{2} \\ = \frac{1}{2} ans$