Question

Find the value of $\underset{x\to 0}{lim}\frac{\sin 2x}{2x^2+x}$.

Answer 1

Now,

$\underset{x\to 0}{lim}\frac{\sin 2x}{2x^2+x}$ $\left(\frac{0}{0}\right)$ form

Now applying L'Hospital's rule we get,

$=\underset{x\to 0}{lim}\frac{2\cos 2x}{4x+1}$

$=\frac{2}{4}$

$=\frac{1}{2}$