Question

Find the limit...

Answer 1

\[\lim_{x \rightarrow 1} (1-\sqrt{2x^2-1})/(x-1)\]

Answer 2

u need to multiply by (1+sqrt(2x^2 -1)) both numerator and denom
thus the question becomes lim (1-(2x^2 -1))/((1+sqrt(2x^2 -1))(x-1))
= lim 2(x+1)(x-1)/((1+sqrt(2x^2 -1))(x-1))
= lim 2(x+1)/ (1+sqrt(2x^2 -1)) [as x<>1}
= 2(1+1)/(1+1) =2 [as x-->1 ]