Mathematics - Limits Question with Solution | TestHub

${\underset{x\to 1}{\lim }\left(\frac{-ax+\sin \left(x-1\right)+a}{x+\sin \left(x-1\right)-1}\right)}^{\frac{1-x}{1- \sqrt{x}}}=\frac{1}{4}$
$\underset{x\to 1}{\lim }{\left(\frac{\frac{\sin \left(x-1\right)}{\left(x-1\right)}-a}{\frac{\sin \left(x-1\right)}{\left(x-\mathrm{<mn>1</mn>}\right)}+1}\right)}^{\left(1+ \sqrt{x}\right)}=\frac{1}{4} \Rightarrow {\left(\frac{1-a}{2}\right)}^2=\frac{1}{4}$
$\Rightarrow$$a=0, a=2$
$\Rightarrow a=0 \left(\sin ce for a =2, base will become -ve \right)$