Question

${lim}_{x\to 0}\frac{(2x+3)(\sqrt{x}-1)}{2x^2+x-3}=$

• A. $1$
• B. $-1$
• C. $2$
• D. $-2$

Answer 1

The correct option is A $1$

$\underset{x\to 0}{lim}\frac{(2x+3)(\sqrt{x}-1)}{2x^2+x-3}$

$=\underset{x\to 0}{lim}\frac{(2x+3)(\sqrt{x}-1)}{(2x+3)(x-1)}$ ...... [Factorising denominator]
$=\underset{x\to 0}{lim}\frac{(2x+3)}{(2x+3)}\times \frac{1}{(\sqrt{x}+1)}$
$=1$