Question

$\underset{x\to 0}{lim}\frac{1-\cos mx}{x^2}$.

Answer 1

${lim}_{x\to 0}\frac{1-\cos mx}{x^2}$ (L-hopital rule)

${lim}_{x\to 0}\frac{m\sin mx}{2x}$ (L-hopital rule)

${lim}_{x\to 0}\frac{m^2\cos mx}{2}⟹\frac{m^2}{2}$