Question

$\underset{x\to 0}{lim}\frac{\cos ax-\cos bx}{\cos cx-\cos dx}$.

Answer 1

${lim}_{x\to 0}\frac{\cos ax-\cos bx}{\cos cx-\cos dx}$ (L-Hopital rule)

${lim}_{x\to 0}\frac{b\sin bx-a\sin ax}{c\sin cx-d\sin dx}$ (L-Hopital rule)

${lim}_{x\to 0}\frac{b^2\cos bx-a^2\cos ax}{c^2\cos cx-d^2\cos dx}⟹\frac{b^2-a^2}{c^2-d^2}$