I'm asked to find the following limit:
$\lim\limits_{x\rightarrow 0} \frac{\sin(3+x)^2-\sin(9)}{x}$
I easily found the solution using L'Hopital's rule as follow:
$\lim\limits_{x\rightarrow 0} \frac{\sin(3+x)^2-\sin(9)}{x}=\lim\limits_{x\rightarrow 0} (6+2x)\cos(3+x)^2=6 \cos(9)=-5,46$
I double-checked my result graphing my function and it works. The problem is that I'm not supposed to know L'Hopital's rule at this time. Is there an alternative way of finding this limit?