Question

If $f\left(x\right)$ is continuous and $f\left(\frac{9}{2}\right)=\frac{2}{9}$, then $\underset{x\to 0}{lim}f\left(\frac{1-\cos 3x}{x^2}\right)$ is equal to :

Answer 1

${lim}_{x\to 0}f\left(\frac{1-\cos 3x}{x^2}\right)={lim}_{x\to 0}f\left(\frac{3\sin 3x}{2x}\right)={lim}_{x\to 0}f\left(\frac{9\sin 3x}{2\left(3x\right)}\right)=f\left(\frac{9}{2}\right)=\frac{2}{9}$