Question

$\underset{x\to 0}{lim}\frac{\sin 2x}{2x^2+x}=$

• A. $0$
• B. $2$
• C. $-1/2$
• D. None of these

Answer 1

Answer: (B)

$2$

$\begin{array}{c}{lim}_{x\to 0}\frac{\sin 2x}{2x^2+x}={lim}_{x\to 0}\frac{\sin \left(2x\right)÷\left(2x\right)}{\left(2x^2+x\right)÷\left(2x\right)}\\ ={lim}_{x\to 0}\frac{\sin \left(2x\right)÷\left(2x\right)}{x+\frac{1}{2}}\\ =\frac{1}{\frac{1}{2}}\\ =2\end{array}$

Hence, option $D$ is the correct answer.