$\underset{x\to 0}{\lim }\frac{e^{ax}-\cos \left(bx\right)-\frac{c.x.e^{-cx}}{2}}{1-\cos \left(2x\right)}=17$ then $5a^2+b^2=$

$\underset{x\to 0}{\lim }\frac{e^{ax}-\cos bx-\frac{cx{e}^{-cx}}{2}}{\frac{2{\sin }^{2}x}{x^2}.x^2}$
$\underset{x\to 0}{\lim }\frac{e^{ax}-\cos bx-\frac{cx.e^{-cx}}{2}}{x^2}ByL.H.rule$
$2a=C$
Again use L. H rule, put x = 0
$\begin{array}{l}\frac{1}{2}(a^2+b^2+\frac{c^2}{2}(1-0+1\left)\right)=34\\ a^2+b^2+c^2=68\\ 5a^2+b^2=68\end{array}$