If $ \lim _{x \rightarrow 0} \frac{e^{a x}-\cos (b x)-\frac{c x e^{-c x}}{2}}{1-\cos (2 x)}=17 $, then $ 5 a^{2}+b^{2} $ is equal to [JEE Main 2023, 13 Apr (Shift 2)]

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If \( \lim _{x \rightarrow 0} \frac{e^{a x}-\cos (b x)-\frac{c x e^{-c x}}{2}}{1-\cos (2 x)}=17 \), then \( 5 a^{2}+b^{2…

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