Q84 / 200 · Manipal (MET) 2011 · Mathematics

$\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}$ is equal to

  • Correct answer
    A
    $-1 / 10$
  • B
    $1 / 10$
  • C
    $-1 / 8$
  • D
    None of these

Solution

$\begin{aligned} & \lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3} \\ &=\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{(2 x+3)(x-1)} \\ & \quad \lim _{x \rightarrow 1} \frac{(2 x-3)}{(2 x+3)(\sqrt{x}+1)} \\ & \quad=\frac{2-3}{(2+3)(\sqrt{1}+1)}=-\frac{1}{10}\end{aligned}$

Hence, the correct answer is option: 'A'.

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