Question

The value of

$\underset{x\to \pi /6}{lim}\frac{2{\sin }^{2}x+\sin x-1}{2{\sin }^{2}x-3\sin x+1}$

• A. $3$
• B. $-3$
• C. $6$
• D. $0$

Answer 1

Answer: (B)

$-3$

We have
$\underset{x\to \pi /6}{lim}\frac{2si{n}^{2}x+sinx-1}{2si{n}^{2}x-3sinx+1}$
$=\underset{x\to \pi /6}{lim}\frac{(2sinx-1)(sinx+1)}{(2sinx-1)(sinx-1)}$
$=\underset{x\to \pi /6}{lim}\frac{sinx+1}{sinx-1}=-3$