Question

$\underset{x\to 0}{lim}\frac{\cos ax-\cos bx}{x^2}=$

Answer 1

${lim}_{x\to 0}\frac{\cos ax-\cos bx}{x^2}\left(\frac{0}{0}form\right)$

Using L-Hopitals rule.

$\Rightarrow \frac{-\sin ax+b\sin bx}{2x}\left(Again{L}^{\prime }Hopita{l}^{\prime }srule\right)\Rightarrow \frac{-a^2\sin ax+b^2\cos bx}{2}\Rightarrow \frac{b^2-a^2}{2}$