Evaluate lim(x→1) (2x-3)(√x-1)/2x^2+x-3

Question

Evaluate

\(\lim\limits_{x \to 1}\frac{(2x-3)(\sqrt x-1)}{2x^2+x-3}\)

Answer 1

\(\lim\limits_{x \to 1}\frac{(2x-3)(\sqrt x-1)}{2x^2+x-3}\)

= \(\lim\limits_{x \to 1}\frac{(2x-3)(\sqrt x-1)}{(2x+3)( x-1)}\)

= \(\lim\limits_{x \to 1}\frac{(2x-3)(\sqrt x-1)(\sqrt x+1)}{(2x+3)(x-1)(\sqrt x+1)}\)

= \(\lim\limits_{x \to 1}\frac{(2x-3)(x-1)}{(2x+3)(x-1)(\sqrt x+1)}\)   [ x ≠ 1]

= \(\lim\limits_{x \to 1}\frac{(2x-3)}{(2x+3)((\sqrt x+1)}\)

= \(\frac{2.1-3}{(2.1+3)(1+1)}\)

= \(\frac{-1}{5.2}\)

= \(-\frac{1}{10}\)