Mathematics - Limits Question with Solution | TestHub

Given limits can be written as,

$\underset{x\to 1}{\mathrm{l}\mathrm{i}\mathrm{m}}\frac{\left(x^2+1\right)\left(x+1\right)\left(x-1\right)}{\left(x-1\right)}=\underset{x\to k}{\mathrm{l}\mathrm{i}\mathrm{m}}\frac{\left(x-k\right)\left(x^2+k^2+xk\right)}{\left(x-k\right)\left(x+k\right)}$
$\Rightarrow 4=\frac{3k^2}{2k}$
$\Rightarrow k=\frac{8}{3}$.